Statistics, probability, and data

Average, Median, and Summary Calculator Summarize a numeric list with its arithmetic mean, median, sum, count, minimum, and maximum. Standard Deviation and Variance Calculator Measure data spread using population or sample standard deviation, with variance and mean. Independent Events Probability Calculator Find the probabilities of both, either, exactly one, or neither of two independent events. Combinations Calculator Count unordered selections of r distinct items from n items without replacement. Z-Score Calculator Express an observation's distance from a mean in standard-deviation units. Permutations Calculator Count ordered arrangements of r distinct items chosen from n. Five-Number Summary and Outliers Minimum, quartiles, median, maximum, IQR, and outlier fences for a data list. Normal CDF (Area Below z) Cumulative standard-normal probability for a z-score, accurate to about 1e-7. Confidence Interval for a Mean Two-sided z-interval for a population mean from sample mean, sd, and size. Correlation Coefficient (r) Pearson correlation between two equal-length numeric lists. Binomial Probability Exact and cumulative probabilities for a fixed number of independent trials. Confidence Interval for a Proportion Wald 95/90/99% interval for a population share from successes and trials. Sample Size for a Mean Respondents needed to hit a margin of error at 90/95/99% confidence. Least-Squares Regression Line Slope, intercept, and fitted equation for paired data. Poisson Probability Exact and cumulative probabilities for counted events at a known average rate. Expected Value (Discrete) Mean outcome of a gamble or lottery from values and probabilities. Sample Size for a Proportion Estimate how many observations a survey needs for a target proportion margin of error and confidence level. Summary Statistics Calculator Find the count, mean, median, mode, and range of a numeric list. Variance and Standard Deviation Calculator Calculate population and sample variance and standard deviation from a numeric list. Binomial Probability Calculator Find the probability of exactly k successes in n independent trials with a fixed success probability. Poisson Probability Calculator Calculate the probability of exactly k events for a Poisson process with a known mean rate. Conditional Probability Calculator Calculate the probability of an event given another event from their joint and conditioning probabilities. Coefficient of Determination Calculator Square a correlation coefficient to express the proportion of linear variation represented by the fitted relationship. Birthday Collision Probability Calculator Calculate the probability that at least two people share a birthday under a uniform-day model. Weighted Average Calculator Calculate a weighted average from comma-separated values and matching nonnegative weights. Moving Average Calculator Calculate simple moving averages from a comma-separated sequence and a selected window size. Acceptance Rate Calculator Calculate acceptance and rejection percentages from the number accepted and the total number of applications or trials. Cohen's d Effect Size Calculator Calculate the standardized mean difference between two independent groups using pooled sample standard deviation. Class Width Calculator Calculate equal histogram class width from a lower boundary, upper boundary, and number of classes. Six-Sided Dice Sum Probability Calculator Calculate the exact probability of a target sum when rolling a selected number of fair six-sided dice. 90% Mean Confidence Interval Calculator Calculate a normal-approximation 90% confidence interval for a sample mean from standard deviation and sample size. 95% Mean Confidence Interval Calculator Calculate a normal-approximation 95% confidence interval for a sample mean from standard deviation and sample size. 99% Mean Confidence Interval Calculator Calculate a normal-approximation 99% confidence interval for a sample mean from standard deviation and sample size. Absolute and Relative Uncertainty Calculator Calculate relative and percentage uncertainty from a measured value and an absolute uncertainty. Classification Accuracy Calculator Calculate accuracy from correct classifications and total evaluated cases. Independent AND Probability Calculator Calculate the probability that two independent events both occur. One-Way ANOVA F Statistic Calculator Calculate between-group and within-group mean squares and the one-way ANOVA F statistic from summary sums of squares and degrees of freedom. Ascending Numeric Order Calculator Parse a short comma- or space-separated list of numbers and return it in ascending order. Bayes Theorem Posterior Probability Calculator Calculate a posterior probability from prior probability, sensitivity, and specificity. Benford First-Digit Probability Calculator Calculate the expected first-digit probability under Benford's logarithmic distribution. Binomial Exact Probability Calculator Calculate the probability of exactly k successes in n independent Bernoulli trials. Five-Number Box Plot Summary Calculator Calculate minimum, first quartile, median, third quartile, and maximum from a numeric list using Tukey hinges. Central Limit Theorem Standard Error Calculator Estimate the standard error and normal-approximation interval for a sample mean. Chebyshev Theorem Coverage Calculator Calculate the guaranteed minimum fraction within k standard deviations of a mean. Exact Coin-Flip Count Probability Calculator Calculate the probability of exactly a selected number of heads in fair coin flips. Confusion Matrix Metrics Calculator Calculate accuracy, precision, recall, specificity, and F1 score from a binary confusion matrix. Normal Continuity Correction Calculator Apply a half-unit continuity correction to a discrete count boundary and convert it to a normal z score. Decile from Numeric Data Calculator Estimate a selected decile from a numeric list using linear interpolation of the sorted positions. Custom Dice Sum Probability Calculator Calculate an exact target-sum probability for a selected number of fair dice with a selected number of sides. Two-Proportion A/B Test Z-Score Calculator Compare two independent proportions with a pooled two-proportion z statistic. Beta Distribution Density Calculator Evaluate the beta probability density and mean for a selected shape pair and value. Chi-Square Goodness-of-Fit Statistic Calculator Calculate a chi-square goodness-of-fit statistic and degrees of freedom from observed and expected counts. Coin Flip Streak Probability Calculator Calculate the probability of seeing at least one run of consecutive heads in fair coin flips. One-Way ANOVA Degrees of Freedom Calculator Calculate total, between-group, and within-group degrees of freedom from sample size and group count. Descriptive Statistics Summary Calculator Calculate population-style mean, median, range, variance, and standard deviation for a finite numeric list. Independent Groups Standardized Difference Calculator Calculate the standardized mean difference between two independent groups using a pooled standard deviation. Independent Measurement Error Propagation Calculator Estimate propagated absolute uncertainty for addition, subtraction, multiplication, or division of two measured values. First Quartile Calculator Calculate the 25th percentile from a finite numeric list using linear interpolation on sorted positions. Grouped Frequency Distribution Calculator Group a finite numeric list into equal-width bins and count the values in each interval. Decimal Odds Implied Probability Calculator Convert decimal odds greater than one into implied probability and percentage. Normal Distribution Point Calculator Calculate a z score, density, and cumulative probability for a point under a normal distribution. Sample Proportion and Standard Error Calculator Calculate a sample proportion and its simple binomial standard error from successes and trials. Two-Sided Normal Z P-Value Calculator Calculate the two-sided standard-normal tail probability associated with a z statistic. Mean Median and Mode Calculator Calculate mean, median, and repeated-value mode information for a finite numeric list. Probability to Odds Calculator Convert a probability below one into odds in favor and log-odds. IQR Outlier Fence Calculator Calculate Tukey outlier fences and classify one value using first and third quartiles. Poisson Exact Count Probability Calculator Calculate the exact probability of observing a selected event count under a Poisson rate model. Mean Squared Error and RMSE Calculator Calculate mean squared error and root mean squared error from equal-length actual and predicted lists. Relative and Percentage Error Calculator Calculate signed relative error and absolute percentage error from an actual value and a nonzero reference. Bertrand Box Conditional Probability Calculator Calculate the probability that a selected coin is gold on the other side after observing a gold face in a three-box paradox model. Boy-or-Girl Conditional Probability Calculator Calculate the probability that both children are girls after a selected at-least-one-girl observation model. Cubic Prediction Polynomial Calculator Evaluate a cubic prediction equation from four supplied coefficients and an input x value. Decimal Odds Probability and Payout Calculator Convert decimal odds to implied probability and calculate total payout and net profit from a stake. Exponential Model Prediction Calculator Evaluate an exponential prediction model from a starting value, continuous rate, and elapsed time. False Positive and Predictive Value Calculator Calculate false-positive rate, positive predictive value, and false discovery rate from prevalence, sensitivity, and specificity. Five-Star Rating Summary Calculator Calculate review count, average star rating, and share of four-or-five-star ratings from star counts. Index of Qualitative Variation Calculator Calculate the index of qualitative variation from category counts. Lower Outlier Fence Calculator Calculate interquartile range and the lower Tukey outlier fence from first and third quartiles. Matthews Correlation Coefficient Calculator Calculate the Matthews correlation coefficient from binary-classification confusion counts. McNemar Paired Proportion Statistic Calculator Calculate the continuity-corrected McNemar chi-square statistic from discordant paired counts. Monty Hall Switching Probability Calculator Calculate stay and switch win probabilities for a generalized Monty Hall game with one prize door. Two-Game Mixed Win-Rate Calculator Calculate the expected win probability for a random mix of two independent games. Proportion Point Estimate Calculator Calculate a sample proportion point estimate and its complement from successes and trials. Process Capability Cp and Cpk Calculator Calculate Cp and Cpk from specification limits, process mean, and process standard deviation. Rayleigh Distribution PDF and CDF Calculator Calculate the probability density, cumulative probability, mean, and standard deviation for a Rayleigh value. Prediction Residual Calculator Calculate signed residual, absolute residual, and squared residual from observed and predicted values. Relative Standard Deviation Calculator Calculate relative standard deviation as a ratio and percentage from standard deviation and mean. Sampling Error Difference Calculator Calculate the signed sampling error between a sample proportion and a supplied population proportion. Expected Risk and Loss Calculator Calculate expected loss from event probability and loss amount, with the complement probability shown. Percentile from a Data List Calculator Estimate a percentile from a sorted or unsorted numeric list using linear interpolation between observations. Interquartile Range Calculator Calculate the interquartile range and midhinge from supplied first and third quartiles. Upper Tukey Fence Calculator Calculate the upper exploratory fence from first and third quartiles using the 1.5-IQR convention. Percentile Rank Calculator Estimate the percentile rank of a target value within a numeric data list, including a transparent tie convention. Trimmed Mean Calculator Calculate a two-sided trimmed mean by removing the same percentage of low and high observations. Mean Absolute Deviation Calculator Calculate the arithmetic mean and the average absolute distance from that mean. Coefficient of Variation Calculator Calculate relative spread by dividing population standard deviation by the absolute arithmetic mean. Standard Error of the Mean Calculator Calculate the standard error and variance of a sample mean from a standard deviation and sample size. Pooled Variance Calculator Calculate pooled variance and pooled standard deviation for two independent groups. Welch Degrees of Freedom Calculator Calculate the Welch–Satterthwaite degrees of freedom for an unequal-variance two-sample mean comparison. Discrete Expected Value Calculator Calculate the expected value and variance of a discrete distribution from paired outcomes and probabilities. Binomial Mean and Variance Calculator Calculate the expected successes, variance, and standard deviation for a binomial model. Geometric Waiting-Time Mean Calculator Calculate the mean and variance of the number of trials until the first success in a geometric model. Odds Ratio from a Two-by-Two Table Calculator Calculate the odds ratio and its natural logarithm from four cells in a two-by-two comparison table. Relative Risk from a Two-by-Two Table Calculator Calculate event risk in two groups and their relative risk from a two-by-two table. Pearson Median Skewness Calculator Calculate Pearson’s second skewness coefficient from the mean, median, and standard deviation. Pooled Two-Sample Degrees of Freedom Calculator Calculate the pooled degrees of freedom for an independent two-sample comparison. Glass’s Delta Effect Size Calculator Calculate Glass’s delta using the control-group standard deviation as the reference scale. Empirical Rule Interval Calculator Calculate one-, two-, and three-standard-deviation intervals and their normal-model coverage percentages. Independent Sum Error Propagation Calculator Calculate the combined absolute and relative uncertainty for a sum or difference of two measured quantities. F-Statistic Calculator Calculate the ratio of two entered variances for a simple F-statistic scenario. Joint Probability Calculator Calculate independent and conditional joint probabilities from event A and event B inputs. Lognormal Distribution Calculator Calculate lognormal density, cumulative probability, reliability, mean, and median from a median scale and shape parameter. Margin of Error Calculator Calculate a normal-approximation margin of error from a critical value, standard deviation, and sample size. Binomial Normal Approximation Calculator Estimate an inclusive binomial count probability using a normal approximation with an optional continuity correction. Sampling Distribution Probability Calculator Calculate the probability that a sample mean falls between two bounds under a normal sampling-distribution assumption. One-Sample Normal Power Calculator Estimate one-sided or two-sided normal-test power from an effect, standard deviation, significance level, and sample size. Three Independent Events Probability Calculator Calculate the probability that three independent events all occur, at least one occurs, or none occurs. Quadratic Regression Calculator Fit a least-squares quadratic y=a+bx+cx² to paired data and evaluate the fitted equation at a target x. Relative Frequency Calculator Convert an observed count into a relative frequency, percentage, and complement within a stated total. Shannon Entropy Calculator Calculate Shannon entropy in bits and min-entropy from a finite probability distribution. Population Skewness Calculator Calculate the Fisher-Pearson population skewness of a finite list of observations. One-Sample t-Statistic Calculator Calculate a one-sample t statistic, standard error, and degrees of freedom from summary statistics. Two-Sample t-Test Statistic Calculator Calculate a two-sample t statistic using either a pooled-variance or Welch unequal-variance standard error. Mann-Whitney U Statistic Calculator Rank two independent samples, calculate the Mann-Whitney U statistics, and show a normal-approximation z score. Weibull Distribution Calculator Calculate Weibull density, cumulative probability, reliability, and mean from shape, scale, and evaluation value. Youden's J Index Calculator Calculate Youden's J from sensitivity and specificity for a binary classification threshold. One-Sample z-Test Statistic Calculator Calculate a one-sample z statistic and two-sided normal p-value when a population standard deviation is supplied. False Positive Base-Rate Calculator Calculate positive predictive value and negative predictive value from prevalence, sensitivity, and false-positive rate. Normal Critical Value Calculator Calculate the two-sided standard-normal critical value for an entered confidence level. Simpson Diversity Index Calculator Calculate Simpson concentration and Gini-Simpson diversity from category counts. Fisher's Exact Test Calculator Calculate an exact two-sided Fisher probability for a 2×2 contingency table with fixed margins. Grouped Data Standard Deviation Calculator Estimate weighted mean and population or sample standard deviation from class midpoints and frequencies. Midrange Calculator Calculate the minimum, maximum, range, and midrange of a numeric data list. Moneyline Odds Calculator Convert a positive or negative moneyline into implied probability, decimal odds, and profit on a fixed stake. OR Probability Calculator Calculate the probability of at least one of two events, exactly one event, and neither event from an overlap. Quartic Regression Calculator Fit a fourth-degree least-squares polynomial to paired data and evaluate it at a target value. Relative Standard Error Calculator Calculate the standard error and relative standard error of a sample mean from a data list. Sum of Squares Calculator Calculate the squared-deviation total, mean squared deviation, and root-mean-square distance from a reference value. Two-Envelope Scenario Calculator Evaluate a transparent two-envelope switching scenario under explicit up/down ratios and a stated probability. Upper Control Limit Calculator Calculate center, upper, and lower three-sigma-style limits for a sample-mean control chart. Raw Score Calculator Convert a z-score into a raw score using a supplied mean and standard deviation. Fractional Odds Calculator Convert fractional odds into decimal odds, implied probability, and profit on a fixed stake. Roulette Payout and House Edge Calculator Estimate win probability, payout, expected net result, and house edge for straight-up or even-money roulette bets. Sample Proportion Probability Calculator Calculate the normal-approximation probability that a sample proportion falls between two bounds. Pie Chart Angle Calculator Convert a category count within a total into a percentage and the central angle for a pie-chart slice. Range Calculator Calculate the minimum, maximum, and total range of a numeric data list. Two-Set Venn Count Calculator Calculate A-only, B-only, union, overlap, and neither counts for two sets inside a stated universe. Five-Number Summary Calculator Sort five observations and report the minimum, first quartile, median, third quartile, and maximum. Combinations Without Repetition Calculator Count how many unordered groups of a chosen size can be selected from a finite set without repeating an item. Mean Confidence Interval Calculator Build a two-sided mean confidence interval from a sample mean, standard deviation, sample size, and supplied critical value. Range and Relative Dispersion Calculator Calculate the range, midrange, and coefficient of range from a positive minimum and maximum. Interquartile Spread (IQR) Calculator Find the interquartile range, midhinge, and quartile spread from the first and third quartiles. Mean Absolute Deviation for Five Values Calculate the mean, mean absolute deviation, and largest absolute deviation for five observations. Median Calculator for Five Values Sort five numeric values and calculate their median, mean, and distance between the extreme values. Minimum, Maximum, and Range Calculator Calculate the span, midpoint, and endpoint ratio from a minimum and maximum observation. Mode Calculator for Five Values Find the unique most frequent value in a five-observation dataset and report its frequency and share. Permutation Calculator Count ordered selections of r distinct items from n available items without repetition. Pooled Standard Deviation Calculator Combine two sample standard deviations using their degrees of freedom to estimate a common pooled spread. Population Variance Calculator Calculate the population mean, population variance, standard deviation, and root-mean-square value for five values. Probability from Favorable Outcomes Convert favorable and total equally likely outcomes into probability, percentage, complement, and odds. Quartile Calculator for Nine Values Sort nine observations and calculate Q1, median, Q3, interquartile range, and the quartile midhinge. Sensitivity Calculator Calculate sensitivity, miss rate, and the number of actual positive cases from true positives and false negatives. Specificity Calculator Calculate specificity, false-positive rate, and the number of actual negative cases from true negatives and false positives. Sensitivity and Specificity Calculator Summarize all four cells of a binary classification table with sensitivity, specificity, accuracy, and prevalence. Sampling Standard Error Calculator Calculate the standard error of a sample mean and an illustrative 95% normal-approximation margin. Two-Dice Sum Probability Calculator Calculate the number of ordered outcomes, probability, percentage, and complement for a target sum from two fair six-sided dice. Measurement Uncertainty Calculator Convert an absolute measurement uncertainty into relative uncertainty, percent uncertainty, and an interval around a measured value. Journal Impact Factor Arithmetic Calculator Calculate the two-year citation rate used in a journal impact-factor style summary from citations and scholarly items, while keeping the metric's scope clear. Third Quartile Calculator Sort a raw dataset and calculate its third quartile, median, first quartile, and interquartile range using a stated median-of-halves convention. Upper and Lower Outlier Fence Calculator Calculate the lower and upper Tukey-style outlier fences from Q1, Q3, and an entered IQR multiplier. Sample or Population Variance Calculator Calculate variance and standard deviation from a pasted dataset while keeping the population or sample divisor explicit. Standard Deviation and Standard Error from Data Calculate a sample standard deviation, standard error of the mean, and relative standard error from raw observations. Histogram Bin Count Calculator Group raw numeric values into equal-width histogram bins and report counts, relative frequencies, and density values. Stem-and-Leaf Plot Calculator Sort raw values into a text stem-and-leaf display while retaining the individual observations. Frequency Polygon Point Calculator Convert class midpoints and frequencies into frequency-polygon points, total frequency, and a grouped weighted mean. Dot Plot Frequency Table Calculator Count repeated values in a raw dataset and produce a sorted dot-plot table with frequencies and proportions. Ordering Numbers Calculator Sort a pasted list from least to greatest and greatest to least, and report the center and endpoints. Pie Chart Percentage Calculator Calculate a category's share, percentage, and pie-slice angle from a category count and total count. Wilcoxon Rank-Sum Statistic Rank two independent samples, calculate the Wilcoxon rank-sum and U statistics, and show a large-sample normal approximation. Inverse Normal Distribution Calculator Find the normal-distribution value at a chosen cumulative percentile from a mean and standard deviation. Post-Test Probability Calculator Use prevalence, sensitivity, and specificity to estimate positive and negative post-test probabilities with Bayes' theorem. One-Sample z Hypothesis Test Calculator Calculate a one-sample z statistic and tail-specific p-value when the population standard deviation is supplied. Least-Squares Linear Regression Calculator Fit a straight line to paired observations and report the slope, intercept, prediction, correlation, and explained variation. Password Combination Calculator Count the exact number of passwords possible from an alphabet size and length, with or without character reuse. Fair Coin Heads Probability Calculator Calculate the probability of an exact or at-least number of heads in repeated fair-coin flips, plus the expected count and spread. Expected Dice Average Calculator Calculate the expected value, variance, standard deviation, and possible range for a sum of fair identical dice. Pie Chart Slice Calculator Turn a list of category values into totals, percentages, and central angles for a complete pie chart. Bertrand Chord Probability Model Calculator Compare the classic probabilities for a chord longer than an inscribed equilateral-triangle side under three explicit random-chord models. Scatter Plot and Linear Regression Calculator Summarize paired x and y data with a correlation coefficient, least-squares line, fitted values, and a transparent prediction. Pearson Correlation Calculator Calculate Pearson’s r, r², means, and supporting sums from paired X and Y observations entered as comma-separated values. Exponential Growth and Decay Calculator Project a positive starting value under discrete compounding or continuous exponential growth and display the change and doubling time. Polynomial Regression Calculator Fit an ordinary least-squares polynomial of degree 1 to 5 to paired observations and report the equation, R², and RMSE. Gender Pay Gap Percentage Calculator Calculate an unadjusted pay gap, comparison-group pay share, and absolute difference from two user-entered earnings figures without bundling stale country data. Lottery Match Probability Calculator Calculate the chance of meeting a chosen lottery match threshold from a pool, ticket size, draw size, and number of tickets without assuming a particular country's game rules. Inverse Standard Normal (z Quantile) Finds the z-score with a given left-tail area under the standard normal curve. Chi-Square Goodness of Fit Tests counts against expected counts with the Pearson chi-square statistic. Empirical Rule Bands 68-95-99.7% intervals from mean and standard deviation. Confidence Interval for a Mean (t) t-interval for the mean when sigma is unknown. Bayes Flip P(A|B) Flips P(B|A) into P(A|B) from the base rate and evidence rate. Root Mean Square Calculate the root mean square of a bounded list of numeric values. Geometric Mean Calculate the geometric mean of a list of positive values using logarithmic accumulation for stability. Harmonic Mean Calculate the harmonic mean of a list of positive values. Bonferroni Correction Calculate a Bonferroni-adjusted significance threshold and adjusted p-value for multiple comparisons. Coefficient of Variation Calculate the sample standard deviation relative to a positive sample mean. Sample Covariance Calculate the sample covariance of two equal-length paired data sets. Spearman Rank Correlation Calculate Spearman's rank correlation for two paired data sets, including average ranks for ties. Geometric Distribution Calculate the probability that the first success occurs on a selected trial and the cumulative probability by that trial. Negative Binomial Distribution Calculate the probability of observing a selected number of failures before a specified number of successes. Median Absolute Deviation Calculate the median and raw median absolute deviation of a numeric sample. Combinations With Repetition Count unordered selections of a fixed size from reusable types, where selecting the same type more than once is allowed. Permutations With Repetition Count ordered sequences of a fixed length from reusable types, where each position may use any type again. Hypergeometric Distribution Calculate an exact and cumulative probability for successes drawn without replacement from a finite population. Continuous Uniform Distribution Evaluate the density and cumulative probability of a continuous uniform variable on a finite interval, with its mean and variance. Exponential Distribution Evaluate the density, cumulative probability, survival probability, mean, and variance of an exponential waiting-time model.

Percentage Calculator Find a percentage of a number, then see the original number with that amount added or subtracted. Percentage Change Calculator Measure the increase or decrease from a positive starting value and compare the absolute change. Fraction Calculator Add, subtract, multiply, or divide two signed fractions and obtain an exact reduced fraction. Quadratic Equation Calculator Solve ax^2 + bx + c = 0 for its real roots and inspect the discriminant. Pythagorean Theorem Calculator Find a missing right-triangle hypotenuse or leg, plus the completed triangle's area and perimeter. Circle Area and Circumference Calculator Calculate a circle's area, circumference, and diameter from its radius. Triangle Area from Three Sides Use Heron's formula to calculate triangle area, perimeter, and the altitude to the first side. Rectangle Area, Perimeter, and Diagonal Calculate floor or panel area, boundary length, and corner-to-corner distance from two sides. Scientific Expression Calculator Evaluate arithmetic expressions with parentheses, powers, square roots, trigonometry, and logarithms. Slope, Distance, and Midpoint Analyze two points: slope of the line, distance between them, and their midpoint. Linear Equation Solver (ax + b = 0) Solve a one-variable linear equation exactly. 2x2 Linear System Solver Solve two equations in two unknowns with Cramer's rule. Trapezoid Area Area of a trapezoid from its two parallel sides and height. Sphere Volume and Surface Area Volume and surface area of a sphere from its radius. Cylinder Volume and Surface Area Volume and total surface area of a right circular cylinder. Exponential Growth and Decay Project discrete or continuous exponential change over time. Arithmetic and Geometric Sequences nth term and partial sum of a sequence from its first term and difference or ratio. Logarithm Calculator Evaluate logarithms in any valid base. Cone Volume and Surface Area Volume and total surface of a right circular cone. Rectangular Box Volume and Diagonal Volume, surface area, and space diagonal of a rectangular box. Right-Triangle Trigonometry Solver Opposite and adjacent sides from hypotenuse and acute angle in degrees. Parabola Vertex and Axis Turning point, axis of symmetry, and opening direction of y = ax^2 + bx + c. 3x3 Linear System Solver Solve three equations in x, y, z with Cramer's rule. Parallelogram Area and Perimeter Area from base and vertical height plus perimeter from side length. GCF and LCM Calculator Find the greatest common factor and least common multiple of two to one hundred whole numbers using exact integer arithmetic. Quadratic Roots Calculator Solve a quadratic equation and show its discriminant and real or complex roots. 2D Distance and Midpoint Calculator Find the straight-line distance and midpoint between two points on a Cartesian plane. Heron’s Triangle Area Calculator Calculate a triangle’s area from its three side lengths and check the triangle inequality. Circle Measurements Calculator Calculate a circle’s diameter, circumference, and area from its radius. Cylinder Volume and Surface Calculator Calculate the volume, lateral area, and total surface area of a right circular cylinder. Percentage Increase Calculator Calculate the absolute and percentage increase from an original value to a new value. Percentage Decrease Calculator Calculate the absolute and percentage decrease from an original value to a lower new value. Percentage Difference Calculator Compare two values using their absolute difference and the average of their magnitudes. Percentage-Point Change Calculator Find the percentage-point change and relative percent change between two rates. Fraction to Percentage Calculator Convert a numerator and denominator into a decimal, percentage, and simplified ratio view. Prime Factorization Calculator Break a positive whole number into its prime factors using exact integer arithmetic. Perfect Number Checker Check whether a positive whole number equals the sum of its proper positive divisors. Circular Sector Calculator Calculate a circular sector’s arc length and area from radius and central angle. Cone Volume and Surface Calculator Calculate the slant height, volume, and closed surface area of a right circular cone. Circular Aperture Area Calculator Calculate the area of a circular opening from its diameter or radius-equivalent diameter input. Azimuth from East and North Components Calculate a compass-style azimuth from east and north coordinate components. Hemisphere Area and Volume Calculator Calculate curved area, total surface area, and volume for a hemisphere from its radius. Ceiling and Floor Function Calculator Calculate the ceiling, floor, and fractional part of a real number. Two-Point Center of Mass Calculator Calculate the one-dimensional center of mass for two point masses at entered coordinates. Quadrilateral Area from Diagonals Calculator Calculate the area of a convex quadrilateral from its two diagonals and the angle between them. Babylonian Base-60 Numeral Converter Convert a nonnegative decimal integer into grouped base-60 positional digits for a simple Babylonian-style notation. Arithmetic Sequence Term and Sum Calculator Calculate a selected term and the finite sum of an arithmetic sequence from its first term and common difference. Donut and Annulus Geometry Calculator Calculate annulus area and cylindrical donut volume from outer radius, inner radius, and height. AAA Triangle Similarity Calculator Scale a triangle with a supplied similarity factor and calculate the new sides and area ratio. Right Triangle Angle and Hypotenuse Calculator Calculate an acute angle and hypotenuse from the opposite and adjacent legs of a right triangle. AAS Triangle Solver Solve the remaining angle and two sides of a triangle from two angles and one opposite side. Clock Hand Angle Calculator Calculate the smaller angle between analog clock hands from an hour and minute value. Binary Division Calculator Divide two nonnegative binary integers with exact binary quotient, remainder, and decimal text output. Absolute and Percentage Change Calculator Calculate signed change and percentage change from an original value to a new value. SAS Triangle Area Calculator Calculate the area and opposite side of a triangle from two sides and their included angle. Binary Fraction Converter Convert a nonnegative binary number with an optional fractional part into its exact decimal value. Binary Multiplication Calculator Multiply two nonnegative binary integers and show the exact binary and decimal products. Box Method Polynomial Multiplication Expand two linear binomials by multiplying the four box terms and collecting like powers. Axis-Aligned Ellipse Center Calculator Find the center of an axis-aligned ellipse from the quadratic and linear coefficients in its equation. Central Angle from Arc Length Calculate a circle's central angle and sector area from radius and arc length. Triangle Classification by Sides and Angles Classify a valid triangle as equilateral, isosceles, or scalene and as acute, right, or obtuse. Least Common Denominator Calculator Find the least common denominator and scaling multipliers for two positive integer denominators. Complementary Angle Calculator Calculate the angle that completes a given angle to a 90-degree complementary pair. Conic Section Classifier Classify a nonrotated quadratic conic from the x-squared, xy, and y-squared coefficients. Exact Decimal to Fraction Calculator Convert a finite decimal text into a reduced fraction without binary floating-point rounding. Quadratic Discriminant Calculator Calculate the discriminant and classify the real-root count of a quadratic equation. Direct Variation Calculator Calculate the output of a direct-variation relationship from its constant and input value. Finite Harmonic Series Calculator Calculate the finite harmonic sum Hₙ = 1 + 1/2 + … + 1/n and a large-n logarithmic approximation. Guitar Fret Position Calculator Calculate distance from the nut and remaining string length for an equal-temperament fret. 2×2 Characteristic Polynomial Calculator Calculate trace, determinant, and characteristic roots for a two-by-two matrix. Collatz Sequence Explorer Generate a bounded Collatz sequence from a positive integer and report steps to one and the maximum visited value. Finite Sequence Convolution Calculator Calculate the linear convolution of two comma-separated finite numeric sequences. 2D Euclidean Distance Calculator Calculate the straight-line distance between two points in a Cartesian plane. Binomial Coefficient Calculator Calculate the exact number of ways to choose k items from n items without regard to order. Logarithm Change-of-Base Calculator Calculate a logarithm in any valid base using natural logarithms. Cartesian to Polar Coordinates Calculator Convert a two-dimensional Cartesian point into radius and angle in polar coordinates. Absolute-Value Linear Equation Calculator Solve an equation of the form absolute value of a times x plus b equals c. Antilogarithm Calculator Calculate a positive base raised to a selected exponent and show the corresponding logarithm inverse operation. Circular Arc Length Calculator Calculate a circular arc length and sector area from radius and central angle in degrees. Inverse Cosine Angle Calculator Calculate the principal inverse-cosine angle in radians and degrees for an input from negative one to one. Inverse Sine Angle Calculator Calculate the principal inverse-sine angle in radians and degrees for an input from negative one to one. Inverse Tangent Angle Calculator Calculate the principal inverse-tangent angle in radians and degrees for a finite ratio. Oblique Triangle Included-Angle Area Calculator Calculate the area of a triangle from two sides and their included angle. Sphere Surface Area and Volume Calculator Calculate the surface area and volume of a sphere from its radius. Coordinate Triangle Area Calculator Calculate the area of a triangle from the x and y coordinates of its three vertices. Average Rate of Change Calculator Calculate the average rate of change between two coordinate points. Coordinate Triangle Centroid Calculator Calculate the centroid coordinates of a triangle from its three vertices. Least Common Multiple Calculator Calculate the greatest common divisor and least common multiple of two positive whole numbers. Fraction Comparison Calculator Compare two signed fractions exactly using cross-products and show their decimal values. Completing the Square Calculator Convert a quadratic polynomial into vertex form and return its vertex from coefficients. Complex Number Operation Calculator Add, subtract, multiply, or divide two complex numbers in rectangular form. Coterminal Angle Calculator Calculate a normalized angle and a selected coterminal angle after an integer number of full turns. Cube Root Calculator Calculate the real cube root of a signed number. Rectangle Diagonal Calculator Calculate the diagonal, area, and perimeter of a rectangle from its side lengths. Geometric Sequence Term and Sum Calculator Calculate a selected term and finite sum of a geometric sequence from its first term and common ratio. Trapezoid Area Calculator Calculate the area of a trapezoid from its two parallel bases and perpendicular height. Polynomial Addition and Subtraction Calculator Add or subtract two polynomials entered as comma-separated coefficients in descending-power order. Two-by-Two Adjoint Matrix Calculator Calculate the adjoint matrix and determinant of a supplied two-by-two matrix. Associative Property Check Calculator Compare the two groupings of three numbers for addition or multiplication. Binary Integer Operation Calculator Apply AND, OR, XOR, or binary addition to two nonnegative binary integers. Two-by-Two Cholesky Decomposition Calculator Factor a symmetric positive-definite two-by-two matrix into a lower triangular matrix and its transpose. Two-by-Two Column Space Calculator Determine the rank, determinant, and a basis description for the column space of a two-by-two matrix. Two-by-Two Infinity-Norm Condition Number Calculator Estimate the infinity-norm condition number of an invertible two-by-two matrix. Three-Dimensional Cosine Similarity Calculator Calculate dot product, cosine similarity, and the angle between two three-dimensional vectors. Two-by-Two Cramer’s Rule Calculator Solve a two-equation linear system with Cramer’s rule and show its determinant condition. Cross-Sectional Area from Volume Calculator Calculate area from a solid’s volume and a perpendicular length, then show the reciprocal volume check. Digital Root Calculator Reduce an integer repeatedly by digit sums until one decimal digit remains. Error Function and Normal-CDF Calculator Approximate erf(x) and the corresponding standard-normal cumulative probability. Floor Division and Remainder Calculator Calculate mathematical floor division and the remainder for two integers, including negative operands. Quadratic Surface Gradient Calculator Calculate the gradient and magnitude for f(x,y)=x²+y² at a supplied point. Two-Dimensional Gram-Schmidt Calculator Orthogonalize two independent two-dimensional vectors and return an orthonormal basis. Two-by-Two Hadamard Product Calculator Multiply corresponding entries of two two-by-two matrices element by element. Square Pyramid Height from Volume Calculator Calculate the perpendicular height of a square pyramid from volume and base side length. Fundamental Counting Principle Calculator Multiply the number of choices at each independent stage of a finite selection process. Hyperbolic Cosine Calculator Evaluate the hyperbolic cosine of a supplied real number. Integer-Order Bessel J Function Calculator Approximate the first-kind Bessel function Jₙ(x) for a small nonnegative integer order. Absolute Value and Sign Calculator Calculate the absolute value, sign, and distance from zero for a real number. Complex Number Rectangular-Form Calculator Calculate rectangular real and imaginary components from a complex magnitude and argument. Bitwise Integer Operations Calculator Calculate bitwise AND, OR, XOR, and left/right shifts for bounded nonnegative integers. Trigonometric Cofunction Calculator Calculate sine and cosine values together with their complementary-angle identities. Rolling Coin Rotation Paradox Calculator Compare center travel and spin counts for a coin rolling around the outside or inside of a fixed circle. Complex Conjugate and Modulus Calculator Calculate the complex conjugate, modulus, and modulus squared of a+bi. Consecutive Integer Sum Calculator Calculate the first and last integer and total sum for a run of consecutive integers. Principal Complex Root Calculator Calculate the principal nth root of a complex number from polar magnitude and argument. Cycloid Arch Geometry Calculator Calculate ideal height, arch length, and area for one cycloid arch generated by a rolling circle. Cyclomatic Complexity Calculator Calculate graph-based cyclomatic complexity from edges, nodes, and connected components. Descartes Rule of Signs Calculator Count coefficient sign changes and report possible positive and negative real-root counts for a polynomial. Symmetric 2×2 Matrix Eigenvalue Calculator Calculate eigenvalues and principal-axis rotation for a real symmetric 2×2 matrix. Diamond Problem Factor Pair Calculator Find the two numbers with a selected sum and product, if the real factor-pair equation has solutions. Positive Divisors and Divisor-Sum Calculator List the positive divisors of a bounded positive integer and calculate their count and sum. Dividing Radicals Numeric Calculator Calculate a quotient of two positive square-root expressions and report its decimal value. Cube Volume Surface Area and Diagonal Calculator Calculate the volume, surface area, and space diagonal of a cube from its side length. Largest Axis-Aligned Cube in a Cylinder Calculator Calculate the largest axis-aligned cube side that fits within a cylinder from cylinder radius and height. Decimal Degrees to Degrees-Minutes-Seconds Calculator Convert a signed decimal degree angle into degrees, arcminutes, and arcseconds. Cotangent from Angle Calculator Calculate sine, cosine, and cotangent for an angle in degrees when cotangent is defined. Distributive Property Expansion Calculator Expand a numerical product across a sum or difference and verify the equivalent total. Point-Slope Line Calculator Build a linear equation and y-intercept from one point and a known slope. Line x-Intercept Calculator Find the x-intercept of a line from its slope and y-intercept. Parallel Line Through a Point Calculator Build the equation of a line parallel to a reference slope through a chosen point. Perpendicular Line Through a Point Calculator Build the equation of a line perpendicular to a nonhorizontal reference slope through a chosen point. Quadratic Function Value Calculator Evaluate a quadratic at a chosen x-value and report its discriminant. Polynomial Evaluation Calculator Evaluate a polynomial from a coefficient list using Horner’s method. Binomial Expansion Term Calculator Calculate one selected term of (a+b)^n using its binomial coefficient. Arithmetic Series Sum Calculator Calculate the final term and total of a finite arithmetic series. Finite Geometric Series Sum Calculator Calculate the final term and total of a finite geometric series. Infinite Geometric Series Limit Calculator Check convergence and calculate the sum of an infinite geometric series when the absolute ratio is below one. Modular Addition Calculator Add two integers and return the least nonnegative remainder under a chosen modulus. Modular Subtraction Calculator Subtract two integers and return the least nonnegative remainder under a chosen modulus. Modular Multiplication Calculator Multiply two integers and return the least nonnegative remainder under a chosen modulus. Modular Division Calculator Solve a modular division by finding the multiplicative inverse when it exists. Regular Polygon Exterior Angle Calculator Calculate each exterior angle and the total exterior turn of a regular polygon. Regular Polygon Area Calculator Calculate the apothem, perimeter, and area of a regular polygon from its side count and side length. Spherical Cap Volume Calculator Calculate the volume of a spherical cap from the sphere radius and cap height. Square Pyramid Slant Height Calculator Calculate the slant height and lateral area of a regular square pyramid. Rhombus Area from Diagonals Calculator Calculate the area and side length of a rhombus from its perpendicular diagonals. Kite Area from Diagonals Calculator Calculate the area of a kite from its perpendicular diagonal lengths. Euler Characteristic of a Convex Polyhedron Calculator Check Euler’s V − E + F relation for a convex polyhedron from its vertices, edges, and faces. Circumscribed Circle of a Regular Polygon Calculator Calculate the circumradius, diameter, and apothem of a regular polygon from its side length and side count. Egyptian Fraction Decomposition Calculator Decompose a positive rational number into a greedy sum of distinct unit fractions. Exponential Notation Calculator Evaluate a mantissa times a power of ten and return its normalized scientific-notation form. Gamma Function Calculator Evaluate the Gamma function Γ(x) and its natural logarithm for a positive real input. Golden Ratio Calculator Calculate the golden ratio and its complementary reciprocal relationships from a positive reference length. Golden Rectangle Calculator Calculate the long side, area, perimeter, and diagonal of a golden rectangle from its short side. Regular Hexagonal Pyramid Surface Area Calculator Calculate the base, lateral, and total surface area of a regular hexagonal pyramid from side length and slant height. Circle Involute Parametric Point Calculator Calculate a point on the involute of a circle from its base radius and unwinding angle. Irregular Polygon Area and Perimeter Calculator Calculate the area and boundary length of a simple irregular polygon from ordered Cartesian vertices. Lagrange Taylor Error Bound Calculator Estimate the Lagrange remainder bound for a Taylor polynomial from derivative bound, distance, and polynomial degree. Trapezoidal Prism Lateral Area Calculator Calculate the lateral area and total surface area of a right trapezoidal prism from its base sides and prism length. Ellipse Latus Rectum Calculator Calculate an ellipse’s semi-latus rectum and full latus-rectum length from semi-major axis and eccentricity. Complex Number to Polar Form Calculator Convert a complex number a + bi into magnitude, radians, degrees, and polar-form notation. Complex Number to Rectangular Form Calculator Convert a complex magnitude and angle into real and imaginary rectangular components. Euclidean Algorithm Trace Calculator Find the greatest common divisor of two whole numbers and show the successive division remainders. Inscribed Angle from Arc Calculator Calculate an inscribed angle from its intercepted arc and show the corresponding central angle. Circle Equation from Diameter Endpoints Calculator Build a circle’s center, radius, and Cartesian equation from the two endpoints of a diameter. Exact Trigonometric Value Calculator Return common exact sine, cosine, and tangent values for standard degree angles, with decimal checks. Conical Frustum Surface Area Calculator Calculate the lateral and total surface area of a right circular conical frustum from its radii and slant height. Circle Center from Three Points Calculator Find the circumcenter and radius of the unique circle through three non-collinear points. Right-Triangle Similarity Calculator Compare the corresponding legs of two right triangles and report their scale-ratio difference. Condense Logarithms Calculator Combine three same-base logarithm terms into one equivalent logarithm and evaluate both forms numerically. Cross-Multiplication Checker Compare two fractions by cross-multiplying their numerators and denominators. Rectangle Dimensions from Area and Perimeter Find the longer and shorter sides and diagonal of a rectangle from its area and perimeter. Double-Angle Identity Calculator Calculate sin(2θ), cos(2θ), and tan(2θ) from the sine and cosine of θ. Engineering Notation Calculator Express a number as a coefficient multiplied by a power of ten whose exponent is a multiple of three. Intersection of Two Lines Calculator Solve two lines in standard form and report their intersection or parallel status. Right Triangle Checker Check three side lengths against the Pythagorean relationship and triangle inequality. 2×2 LU Decomposition Calculator Decompose a 2×2 matrix into lower-unit and upper-triangular factors and verify their determinant. 2D Vector Independence Calculator Determine whether two two-dimensional vectors are linearly independent from their determinant. 2×2 Null Space Calculator Check a 2×2 matrix determinant and return a representative null vector when the matrix is singular. Expand Logarithms Calculator Expand a logarithm of powered factors into a weighted sum of same-base logarithms and evaluate both forms. Three-Side Triangle Area Calculator Find the area, perimeter, semiperimeter, and inradius of a triangle when all three side lengths are known. ASA Triangle Solver Solve an angle-side-angle triangle from two angles and the side opposite the first angle. Triangle Centroid Calculator Find the centroid of a triangle from the coordinates of its three vertices and report its area. Complex Number to Trigonometric Form Convert a complex number from rectangular real-plus-imaginary form into magnitude and angle form. Cone Surface Area Calculator Calculate the slant height, base area, lateral area, and total surface area of a right circular cone. Cone Volume Calculator Calculate the volume and base area of a right circular cone from its radius and vertical height. Coordinate Distance and Midpoint Calculator Find the horizontal change, vertical change, straight-line distance, and midpoint between two Cartesian points. Ellipse Perimeter and Area Calculator Estimate an ellipse’s perimeter with Ramanujan’s approximation and calculate its area and eccentricity. Equivalent Ratio Calculator Solve the missing denominator in a proportion of the form a:b = c:x and verify the resulting ratio. Greatest Common Divisor Calculator Find the greatest common divisor, least common multiple, and reduced positive ratio of two whole numbers. Right-Triangle Hypotenuse Calculator Calculate the hypotenuse, area, perimeter, and acute angle of a right triangle from its two legs. Isosceles Triangle Height Calculator Find the height, area, perimeter, and base angles of an isosceles triangle from its equal side and base. Parallelogram Area and Perimeter Calculator Calculate a parallelogram’s area from its base and perpendicular height, then report its perimeter from the side length. Regular Polygon Calculator Calculate the perimeter, apothem, interior angle, and area of a regular polygon from its side count and side length. Rhombus Area and Perimeter Calculator Calculate a rhombus’s area, side length, perimeter, and acute angle from its two diagonals. 2D Point Rotation Calculator Rotate a Cartesian point about the origin and report its new coordinates, radius, and direction. Trapezoid Midsegment Calculator Find the segment joining the midpoints of a trapezoid’s legs, along with its base average and area. Truncated Cone Volume Calculator Calculate the volume, slant height, lateral area, and total surface area of a right circular truncated cone. 2D Vector Resultant Calculator Add two two-dimensional vectors and calculate the resultant components, magnitude, dot product, and cross-product z component. Vector Direction and Unit Vector Calculator Find a vector’s magnitude, direction angle, and unit-vector components from its x and y components. Mayan Numeral Converter Convert a non-negative decimal integer into the place-value digits and readable dot-and-bar notation of the Maya vigesimal numeral system. Möbius Strip Geometry Calculator Estimate the exact-parametrization surface area and boundary length of a one-half-twist Möbius strip from its centerline radius and half-width. Sinusoidal Phase-Shift Calculator Analyze a transformed sine or cosine function to find amplitude, period, horizontal phase shift, midline, and the value at a chosen x-coordinate. Prisoner’s Dilemma Payoff Calculator Test a symmetric two-player payoff set for the strict Prisoner’s Dilemma ordering and identify dominant defection and the one-shot Nash outcome. M/M/1 Queueing Calculator Calculate utilization, idle probability, average queue lengths, and waiting times for a stable single-server M/M/1 queue. Rational Zeros Theorem Calculator List rational-root candidates for an integer polynomial and test them exactly to identify the rational zeros of a linear, quadratic, or cubic polynomial. Significant Figures Calculator Round a measured or calculated value to a chosen number of significant figures while keeping the scientific-notation result visible. Terminating Decimal Checker Reduce a fraction, factor its denominator, and determine whether its base-10 decimal expansion terminates and how many places it needs. Logic Truth Table Calculator Evaluate a selected two-input Boolean connective for a chosen row and display the complete truth table for AND, OR, XOR, NAND, NOR, XNOR, or implication. Two’s Complement Converter Encode a signed integer into a fixed-width two’s-complement bit pattern and decode the same pattern back to its signed and unsigned values. Adding and Subtracting Fractions Add or subtract two fractions with a least-common-denominator walkthrough, reduced exact answer, mixed-number form, and decimal check. Binary Subtraction Calculator Subtract signed binary numbers, inspect the decimal check, see aligned operands, and encode the result in a chosen two’s-complement width when it fits. Crescent and Circle-Overlap Area Calculator Calculate the overlap and the two lune-shaped remainder areas formed by two intersecting circles, and identify which lune is a crescent. Interior and Exterior Triangle Angles Enter two interior angles of a triangle to find the missing interior angle, the three adjacent exterior angles, and both angle-sum checks. Cubic Equation Solver Solve a real cubic equation for all three roots, including repeated and complex-conjugate roots, and classify the root pattern with the cubic discriminant. 2×2 Eigenvalue and Eigenvector Calculator Find the trace, determinant, eigenvalues, and representative eigenvectors of a general real two-by-two matrix, including complex eigenvalues. Doubling Time Calculator Find how long a quantity takes to double under a constant percentage growth rate, or find the periodic rate needed to double in a chosen time. Average Percentage Calculator Find both the ordinary mean and the sample-size-weighted mean of a list of percentages so grouped survey or test results are not averaged incorrectly. Fractional Exponent Calculator Evaluate a base raised to a rational exponent, reduce the exponent fraction, show the equivalent root-power form, and reject non-real branches clearly. Compatible Numbers Estimator Round numbers to an easy place value for quick mental arithmetic, then compare the compatible-number estimate with the exact operation and its error. Gauss-Jordan Linear System Solver Solve a small square system of linear equations from a coefficient matrix and right-hand-side vector using reduced row echelon elimination. Linear Feedback Shift Register Sequence Step a binary Fibonacci-style LFSR with an explicit seed, tap list, and number of transitions. Odd-Order Magic Square Generator Generate the classic odd-order normal magic square and verify its common row, column, and diagonal sum. Negative Modulo Convention Calculator Compare Euclidean and truncating division results for negative dividends so the remainder convention is visible instead of assumed. Base-2 Logarithm Calculator Find the binary logarithm of a positive number and show the equivalent natural and common logarithms. Triangle Midsegment Calculator Find the segment joining the midpoints of two triangle sides and verify its parallel-side and scale relationships. Rectangle Dimensions from Perimeter Recover rectangle length and width from a known perimeter and a chosen length-to-width ratio. Hyperbolic Function Calculator Evaluate sinh, cosh, tanh, and the reciprocal hyperbolic functions for a real input. Long Addition with Carry Steps Add two nonnegative whole numbers and show the aligned decimal result and carry count using exact integer arithmetic. Long Multiplication with Partial Products Multiply two nonnegative whole numbers exactly and display the shifted partial products used by the column method. Divide Powers with the Same Base Simplify and evaluate a quotient of two powers that share the same nonzero base. Expanded Form of a Whole Number Rewrite a signed whole number as the sum of its nonzero place-value terms and find its digit sum. Test Associativity in Modular Arithmetic Compare both groupings of addition and multiplication after reducing integers modulo a positive modulus. Find the Missing Endpoint from a Midpoint Find the second endpoint of a line segment when one endpoint and the midpoint are known, with length and slope checks. Long Subtraction with Borrowing Subtract two nonnegative whole numbers exactly, show the signed difference, and count the borrowing steps. Rational or Irrational Number Classify a fraction or a principal square root as rational or irrational and show the reduced form. Relatively Prime Numbers Find the greatest common divisor, least common multiple, and Bézout coefficients to test whether two integers are coprime. Reference Angle Normalize an angle, identify its quadrant or axis, and calculate the reference angle with sine, cosine, and tangent checks. Power Set of a Finite Set List every subset of a small finite set and calculate the power-set cardinality 2ⁿ. Powers of i Reduce an integer power of the imaginary unit i using its four-step cycle and return its real and imaginary parts. Direct and Power Variation Constant Find the constant of proportionality and predict a target value for a direct or power-variation relationship. Area of a Circle Calculator Find the area, diameter, and circumference of a circle from its radius. Circumference Calculator Calculate a circle's circumference, radius, and area from its diameter. Cube Volume and Surface Area Calculator Calculate the volume, surface area, face area, and total edge length of a cube. Regular Pentagon Calculator Calculate the perimeter, apothem, circumradius, area, and interior angle of a regular pentagon from its side length. Regular Hexagon Calculator Calculate the perimeter, apothem, circumradius, area, and interior angle of a regular hexagon from its side length. Regular Octagon Calculator Calculate the perimeter, apothem, circumradius, area, and interior angle of a regular octagon from its side length. 30-60-90 Triangle Calculator Find every side, area, perimeter, and trigonometric ratio of a 30-60-90 right triangle from any one known side. Order of Magnitude Calculator Express a nonzero value in scientific notation and identify the nearest power of ten that describes its scale. Greater Than or Less Than Calculator Compare two numbers and show their exact ordering, signed difference, absolute difference, minimum, and maximum. Quaternion Arithmetic and Rotation Calculator Multiply two quaternions, inspect norms, conjugates, inverses, and rotate a 3D vector with a normalized quaternion. Subset and Set Difference Calculator Check whether one finite set is a subset or proper subset of another and list the elements missing from either direction. Union, Intersection, and Symmetric Difference Calculator Calculate the union, intersection, directional differences, symmetric difference, and cardinality relationship of two finite sets. 2×2 Singular Value Decomposition Calculator Compute the singular values, orthonormal U and Vᵀ factors, rank, condition number, and reconstruction error of a real 2×2 matrix. Pascal's Triangle Entry Calculator Find an exact binomial coefficient in Pascal's triangle and the sum of the selected row. Generalized Harmonic Number Calculator Calculate a finite generalized harmonic sum and show the last-term and average-term contributions. Two-Factor Partial Fraction Decomposition Calculator Decompose a rational expression with two distinct linear denominator factors and verify its value at a chosen x. 2D Vector Linear Combination Calculator Solve for the two coefficients that express a target 2D vector as a linear combination of two supplied vectors. Square Pyramid Block Count Calculator Count the unit blocks in a stepped square pyramid whose layers have side lengths from one block through the entered base side. Interval Notation Converter Build an interval and its matching inequality from finite or unbounded endpoints, endpoint inclusion, and an open or closed boundary choice. FOIL Binomial Expansion Calculator Expand two linear binomials, return the normalized quadratic coefficients, discriminant, and real or complex roots when the product is treated as an equation equal to zero. Negative Exponent Calculator Evaluate a nonzero base raised to a negative whole-number exponent and show the reciprocal relationship step by step. 2×2 Moore–Penrose Pseudoinverse Calculator Calculate a transparent Moore–Penrose pseudoinverse for a real 2×2 matrix, including full-rank, rank-one, and zero-matrix cases. Rise Over Run Slope Calculator Calculate rise, run, slope, direction angle, and y-intercept from two Cartesian points, while identifying a vertical line safely. Nearest Integer Rounding Calculator Round a real number to an integer using either half-away-from-zero or half-to-even tie handling, with the rounding distance shown. Two-Circle Triangulation Calculator Find the two possible planar intersection points from a baseline and two distances, exposing mirror-image ambiguity and the tangent case. Triangle Angle-Type Classifier Classify a triangle from its three side lengths and calculate its largest angle, perimeter, and semiperimeter. Oblique Triangle Area Calculator Calculate the area, third side, and altitude of an oblique triangle from two sides and their included obtuse angle. Triangle Base from Area and Height Solve for a triangle's base when its area and perpendicular height are known, then verify the area relationship. Triangle Interior and Exterior Angles Complete a triangle from two interior angles and calculate the adjacent exterior angles and their total. Coordinate Midpoint and Segment Calculator Find the midpoint, coordinate changes, and straight-line length between two points in a Cartesian plane. Heron's Formula Triangle Area Calculate a triangle's area, semiperimeter, perimeter, and inradius from its three side lengths. Equilateral Triangle Geometry Calculator Calculate the area, perimeter, height, inradius, and circumradius of an equilateral triangle from its side length. Regular Decagon Area and Geometry Calculate the area, perimeter, apothem, circumradius, and interior angle of a regular decagon from its side length. Regular Dodecagon Area and Geometry Calculate the area, perimeter, apothem, circumradius, and interior angle of a regular dodecagon from its side length. Regular Heptagon Area and Geometry Calculate the area, perimeter, apothem, circumradius, and interior angle of a regular heptagon from its side length. Regular Hexagonal Pyramid Volume Calculator Calculate the base area, volume, perimeter, apothem, and slant height of a regular hexagonal pyramid from its side and vertical height. Triangle Proportionality Theorem Calculator Solve a missing side segment when a line parallel to a triangle base creates two proportional smaller sides. Triangle Congruence by Side Lengths Compare two triangles by their three side lengths, test SSS congruence, and compare perimeter and area. Triangle Scale Factor and Area Change Calculate a triangle's linear scale factor and project how its perimeter and area change under a similar enlargement or reduction. 2×2 QR Decomposition Calculator Factor a nonsingular real 2×2 matrix into an orthogonal Q matrix and an upper-triangular R matrix, then check reconstruction and orthogonality errors. 2×2 Polar Decomposition Calculator Decompose an invertible real 2×2 matrix into an orthogonal factor Q and a symmetric positive-definite stretch factor H, with error checks for A = QH. 2D Vector Tensor Product Calculator Calculate the outer tensor product of two real two-dimensional vectors and report its four components, Frobenius norm, and rank-one consistency check. 3×4 Reduced Row-Echelon Form Calculator Transform a real 3×4 matrix into reduced row-echelon form with partial pivoting, then report rank and pivot columns without interpreting the matrix as a system solution. Cubic by Quadratic Polynomial Division Calculator Divide a cubic polynomial by a quadratic polynomial and return the linear quotient, linear remainder, and an identity check. Polynomial Graphing Sample Calculator Evaluate a polynomial across an evenly spaced interval and return a compact table for sketching its graph. Rectangle Diagonal and Angle Calculator Calculate a rectangle’s diagonal, diagonal angle, area, and perimeter from its length and width. Trapezoidal Prism Volume Calculator Calculate the volume of a right trapezoidal prism from its two parallel bases, trapezoid height, and prism length. Surface Area to Volume Ratio Calculator Calculate surface area, volume, and their ratio for a cube, sphere, or right circular cylinder. Galileo’s Paradox Finite Demonstration Count positive integers and perfect squares up to a finite limit to demonstrate the pairing behind Galileo’s infinity paradox without pretending to measure infinity. Hilbert’s Hotel Mapping Calculator Explore finite guest shifts and the classic countably infinite room mappings used to explain Hilbert’s hotel thought experiment. Multiplying Polynomials Calculator Multiply two polynomials from coefficient lists, combine like powers, and inspect every resulting coefficient. Elimination Method Calculator Solve a two-equation linear system by scaling and adding equations to eliminate the y variable, with the arithmetic shown. Substitution Method Calculator Solve a two-equation linear system by isolating y in the first equation, substituting into the second, and checking the ordered pair. One-Dimensional Inequality Graphing Calculator Solve a linear inequality, write its interval, and sample a visible x-window to make the open or closed endpoint and direction easy to check. Fundamental Trigonometric Identities Checker Check a supplied sine and cosine pair against the Pythagorean identity and calculate tangent and reciprocal identities when defined. Rationalize Denominator Calculator Remove one square-root term from a numeric denominator by multiplying by its conjugate, then show the equivalent radical form and a numeric check. Segment Addition Postulate Calculator Find a whole segment or a missing adjacent part from two segment lengths, with a closure check that makes the relationship visible. Triangle Inequality Calculator Check whether three positive lengths can form a non-degenerate triangle, show every inequality slack, and calculate Heron area when valid. Floor and Ceiling Function Calculator Compare floor, ceiling, truncation, fractional part, and an explicit nearest-integer rule for a real number, including negative values. Polish Notation and RPN Calculator Convert a bounded arithmetic expression from infix form to prefix Polish notation and postfix reverse Polish notation, then evaluate it without executing arbitrary code. Derivative at a Point (Central Difference) Estimates f'(a) from two nearby function values using the symmetric central-difference quotient. Simpson's 1/3 Rule Integral Approximates a definite integral from endpoint and midpoint values with one Simpson panel. Tangent Line Equation Builds the tangent line at x = a from the function value and derivative. Linear Inequality Solver Solves ax + b against zero and reports the ray solution with its boundary point. Quadratic Factoring Helper Reports the discriminant, root nature, and real roots of ax^2 + bx + c. Complex Number Arithmetic Adds, subtracts, multiplies, or divides two complex numbers and reports the magnitude. Variation Solver Evaluates direct, inverse, and joint variation models from the constant k. Absolute Value Equation Solver Solves |ax + b| = c by splitting into the positive and negative cases. Triangle Angles from Three Sides (Law of Cosines) All three interior angles of a triangle from its side lengths a, b, c. Circular Arc Length and Sector Area Arc length and sector area from a radius and central angle in degrees or radians. Ellipse Area Area enclosed by an ellipse from its semi-major and semi-minor axes. Completing the Square Vertex form a(x-h)^2+k and vertex (h, k) for a quadratic. Cubic Critical Points Stationary x-values where the derivative of a cubic is zero. Riemann Sums Left, right, and trapezoidal sums from evenly spaced heights. Polar Coordinate Converter Convert polar (r, degrees) to rectangular (x, y) and back. Average Rate of Change Secant slope (f(b)-f(a))/(b-a) between two points. Regular Polygon Area Area of a regular n-gon from side count and side length. Map Scale Distance Ground distance in cm, m, and km from a map length and 1:N scale. Synthetic Division Divide a polynomial by (x - c) in one row: quotient plus remainder. Ratio Test for Series Judge absolute convergence from consecutive-term ratios. Unit Circle Values Exact-feel sin, cos, tan for common angles via trig. Law of Sines (ASA Triangle) Solve a triangle from two angles and the side opposite A. Area Between Two Curves (Simpson) Approximates area between sampled top and bottom curves with one Simpson panel. Midpoint Riemann Sum Estimates a definite integral from function values sampled at the midpoint of each equal subinterval. Hemisphere Geometry Calculate a hemisphere's volume, curved surface area, and total surface area from its radius. Ellipsoid Volume Calculate the volume of an ellipsoid from its three semi-axis lengths. Pyramid Volume Calculate the volume of a pyramid from its base area and perpendicular height. Conical Frustum Volume Calculate the volume of a right circular frustum from its two radii and perpendicular height. Semicircle Geometry Calculate the area, curved arc length, and full perimeter of a semicircle from its radius. Kite Area Calculate the area of a kite from the lengths of its perpendicular diagonals. Coordinate Triangle Area Calculate a triangle's area and orientation from the Cartesian coordinates of its three vertices. SAS Triangle Area Calculate a triangle's area from two sides and their included angle. Triangle Centroid Find the centroid of a triangle from the Cartesian coordinates of its three vertices. 3D Vector Cross Product Calculate the cross product and magnitude of two three-dimensional Cartesian vectors. Fibonacci Number Calculate an exact Fibonacci number using F0=0, F1=1, and integer recurrence. Volume of a Parallelepiped Calculate the volume of a parallelepiped from three edge vectors. Divisibility Test Test whether one whole number divides another without a remainder. Factorial Calculate an exact nonnegative-integer factorial. Perfect Square Test Check whether a nonnegative whole number is the square of an integer. Perfect Cube Test Check whether a signed whole number is the cube of an integer. Prime Number Test Test whether a whole number is prime and report its smallest factor. Pythagorean Triples List integer right-triangle side triples up to a selected hypotenuse limit. Triangular Numbers Calculate the exact nth triangular number from a nonnegative index. Chinese Remainder Theorem Solve two simultaneous congruences with coprime positive moduli. Modular Multiplicative Inverse Find the integer that multiplies a value to 1 modulo a coprime modulus. Modular Exponentiation Calculate a nonnegative integer power modulo a positive modulus. Fermat's Little Theorem Check Check the modular result described by Fermat's little theorem for a prime modulus. Sum of Digits Add the decimal digits of a signed whole number without losing large integer digits. 3D Dot Product Calculate the scalar dot product of two three-dimensional Cartesian vectors from their six ordered components. Angle Between Two 3D Vectors Find the principal angle in degrees between two nonzero three-dimensional Cartesian vectors. 3D Vector Addition Add two three-dimensional Cartesian vectors component by component and return the summed x, y, and z values. 3D Vector Magnitude Calculate the Euclidean L2 magnitude of a three-dimensional vector from its x, y, and z components. 3D Unit Vector Normalize a nonzero three-dimensional Cartesian vector to a vector of Euclidean length one. Projection of One 3D Vector onto Another Calculate the vector projection of A onto nonzero vector B from their ordered three-dimensional components. Linear Interpolation Estimate y at an in-range x between two ordered points using a straight-line interpolation fraction. Bilinear Interpolation Interpolate a value inside an ordered rectangle from four finite corner values and an in-range x-y target. Equation of a Plane from a Normal and Point Build the Cartesian equation of a plane from a nonzero normal vector and one point on the plane. Distance from a Point to a Plane Calculate the unsigned and signed Cartesian distance from a point to a plane given by ax + by + cz + d = 0. Circumcenter of a 2D Triangle Find the Cartesian circumcenter and circumradius of a non-collinear triangle from its three ordered vertices. Orthocenter of a 2D Triangle Find the Cartesian orthocenter of a non-collinear triangle from its three ordered vertices. 3D Euclidean Distance Calculate the straight-line Euclidean distance between two ordered points in a three-dimensional Cartesian coordinate system. 3D Manhattan Distance Calculate the axis-aligned Manhattan distance between two ordered points in a three-dimensional Cartesian coordinate system. Circle Chord Length Find the straight chord length determined by a circle radius and a minor central angle measured in degrees. Great-Circle Distance Calculate the shortest spherical-surface distance and central angle between two latitude-longitude points on a sphere. Cartesian to Spherical Coordinates Convert one non-origin Cartesian point into radial distance, azimuth, and polar angle with degree outputs. Catenary Curve Height Evaluate the height of the canonical symmetric catenary y = a cosh(x/a) at a selected horizontal coordinate. Ring Torus Volume Calculate the volume of a non-self-intersecting ring torus from its major radius and smaller tube radius. Convex Trapezoid Perimeter Add the two parallel bases and two legs of a nondegenerate convex trapezoid after checking that the four lengths can form the shape. Regular Polygon Interior Angle Calculate one interior angle of a regular polygon from its whole-number count of sides. Minor Circular Segment Area Calculate the area between a circle chord and its minor arc from radius and included central angle. Absolute-Value Inequalities Solve |a*x+b| in relation to a nonnegative threshold and report the interval or solution meaning explicitly. Line Equation From Two Points Construct a normalized A*x+B*y+C=0 line from two distinct two-dimensional Cartesian points, including vertical lines. Circle Equation Build the standard circle equation from a center and positive radius, then return the expanded quadratic coefficients. 3x3 Matrix Determinant Calculate the determinant of a bounded finite numeric 3x3 matrix in row-major order. Ellipse Standard Form Construct the standard axis-aligned ellipse equation from a center and positive horizontal and vertical semiaxes. Foci of an Ellipse Find the focal distance, horizontal foci, and eccentricity from an ellipse center, semimajor axis, and semiminor axis. Ellipse Circumference Approximation Estimate the circumference of an ellipse with the clearly labeled Ramanujan II approximation and its shape parameter. Cylindrical Coordinates Convert Cartesian x, y, z coordinates to cylindrical rho, normalized azimuth, and unchanged z. Line of Intersection of Two Planes Find one finite point and a direction vector for the intersection line of two nonparallel planes. Hollow Cylinder Volume Calculate the material volume of a uniform hollow cylinder from outer radius, inner radius, and height. Torus Surface Area Calculate the surface area of an ordinary ring torus from its major and minor radii. Trapezoid Height Find the perpendicular height implied by two parallel bases and a positive trapezoid area. Regular Polygon Perimeter Calculate the perimeter of a regular polygon from an integral side count and common side length. Surface Area of a Triangular Prism Calculate the total surface area of a straight triangular prism from three valid base sides and prism length. Regular Tetrahedron Volume Calculate the volume of a regular tetrahedron from its common edge length. Matrix Addition Add two finite row-major 3x3 matrices entry by entry and return their deterministic matrix sum. Matrix by Scalar Multiply every entry of one finite row-major 3x3 matrix by one bounded scalar. Matrix Multiplication Multiply two finite row-major 3x3 matrices using ordered row-column dot products. Matrix Transpose Transpose a finite row-major 3x3 matrix by exchanging its row and column indices. Matrix Trace Sum the three main-diagonal entries of a finite row-major 3x3 matrix. Matrix Norm Calculate the Frobenius norm of a finite row-major 3x3 matrix from all nine squared entries. Matrix Power Raise a finite row-major 3x3 matrix to a bounded whole-number exponent from 0 through 12. Matrix Rank Estimate the numerical rank of a finite row-major 3x3 matrix with a documented scale-relative pivot tolerance. Cofactor Matrix Construct the signed 3x3 cofactor matrix of a finite row-major matrix from its nine 2x2 minors. Matrix Inverse Calculate the inverse of a finite row-major 3x3 matrix through the determinant and adjugate identity with stability checks. Random Number Generator Generate bounded whole numbers with optional uniqueness for simulations and classroom exercises. Dice Roller Roll one or more equal-sided dice and show every roll, the total, and the average. Factor and Prime Factorization Calculator List the positive factors and prime factorization of a nonzero integer. Common Factor Calculator Find the greatest common factor and every positive factor shared by a list of integers. Rounding Calculator Round a number to decimal places with explicit half-up, half-even, floor, ceiling, or toward-zero rules. Root Calculator Calculate real nth roots, including odd roots of negative values. Exponent Calculator Evaluate a real base raised to a real exponent with finite-domain validation. Ratio Calculator Solve the missing fourth term in a:b = c:x and show the equivalent ratio. 2x2 Matrix Calculator Calculate the determinant or inverse of a two-by-two matrix with the defining formula shown. Big Number Calculator Perform exact signed-integer arithmetic without converting large inputs to floating-point numbers. Long Division Calculator Divide signed whole numbers exactly and continue the quotient to a requested number of decimal places.

Uniform Acceleration Motion Find final velocity and displacement from initial velocity, constant acceleration, and time. Newton's Second Law Force Calculate force from mass and acceleration, the core relation of classical dynamics. Kinetic Energy Compute the energy of motion from mass and speed. Gravitational Potential Energy Estimate stored energy from mass, height, and Earth's gravity. Work and Power Find mechanical work from force and distance, and power from work over time. Ohm's Law Solver Solve for voltage, current, or resistance in a simple resistive circuit. Density, Mass, and Volume Solver Solve the density relation for whichever of the three quantities is unknown. Molarity Calculator Find solution concentration from moles of solute and litres of solution. Solution Dilution (M1V1 = M2V2) Find the concentration after diluting a stock solution to a new volume. Ideal Gas Law Solver Solve PV = nRT for pressure, volume, moles, or temperature. pH and Hydrogen Ion Calculator Convert between hydrogen-ion concentration and pH in either direction. Free-Fall Time and Impact Speed Drop time and impact velocity for a height with no air resistance. Linear Momentum Momentum from mass and velocity, with kinetic energy for context. Electric Power (P = VI) Power dissipated from voltage and current. Specific Heat Energy (Q = mcT) Thermal energy to change a mass's temperature. Combined Gas Law Solver Find the missing pressure, volume, or temperature between two gas states. 1:1 Titration Concentration Unknown concentration from a 1:1 mole-ratio titration. Solution Preparation Mass Solute mass needed for a target molarity and volume. Projectile Range (Level Ground) Horizontal range of a launch that lands at launch height, vacuum model. Series and Parallel Resistance Equivalent resistance of a resistor list in series or parallel. Wave Speed, Frequency, and Period Relate wave speed, frequency, wavelength, and period. Reaction Percent Yield Efficiency of a chemical reaction from actual vs theoretical product. Moles and Mass Converter Convert between grams and moles with a user-entered molar mass. pH to pOH and Hydroxide Complete the pH/pOH pair plus hydroxide concentration at 25 C. Hardy-Weinberg Genotype Frequencies Genotype frequencies from one allele frequency under equilibrium. Exponential Population Growth Project a population with constant per-capita growth rate. Percent Error Calculator Compare a measured value with a reference value using absolute, percent, and signed percent error. Ideal Gas Pressure Calculator Calculate ideal-gas pressure from amount, temperature, and volume using consistent SI-compatible inputs. Specific Heat Energy Calculator Calculate thermal energy transferred when a material changes temperature. Wavelength and Frequency Calculator Find wavelength, frequency, period, and angular frequency for a periodic wave. Uniform Acceleration Calculator Calculate acceleration, average velocity, and displacement when initial and final velocity are known. Projectile Motion Calculator Estimate flight time, horizontal range, and maximum height for ideal level-ground projectile motion. Boyle’s Law Calculator Find a gas’s unknown pressure or volume when temperature and amount stay constant. Resistance and Electrical Power Calculator Calculate resistance and power from voltage and current using Ohm’s law. Capacitance and Stored Energy Calculator Calculate capacitance and stored energy from charge and voltage. Reynolds Number Calculator Calculate the dimensionless Reynolds number for a flow from density, speed, length, and dynamic viscosity. Reaction Percent Yield Calculator Compare actual product yield with theoretical yield as a percentage. Air Pressure at Altitude Calculator Estimate pressure at altitude with an isothermal ideal-gas atmosphere model. Acceleration from Force and Mass Calculator Calculate acceleration from a net force and an object’s mass using Newton’s second law. Angle of Repose Calculator Estimate the limiting angle of repose from a static friction coefficient. Angular Displacement Calculator Calculate angular displacement and revolutions from constant angular velocity and elapsed time. Angular Frequency Calculator Convert ordinary frequency into angular frequency and period for a repeating cycle. Ideal Air Density Calculator Estimate ideal dry-air density from absolute pressure and temperature. Exponential Attenuation Calculator Calculate remaining intensity and attenuation in decibels for an exponential-loss model. Bulk Modulus Calculator Calculate a material’s bulk modulus from pressure change and fractional volume change. Absolute Humidity Calculator Calculate absolute humidity from water-vapor mass and the volume of air containing it. Acoustic Impedance Calculator Calculate characteristic acoustic impedance from medium density and sound speed. Ballistic Coefficient Calculator Calculate a simplified ballistic coefficient from mass, drag coefficient, and reference area. Bernoulli Equation Calculator Find downstream pressure from two flow states with a steady incompressible Bernoulli model. Two-Body Calorimetry Calculator Estimate the equilibrium temperature when two bodies with known masses and specific heats exchange heat in an isolated model. Blackbody Radiation Power Calculator Estimate thermal radiation power from area, absolute temperature, and emissivity using the Stefan–Boltzmann model. Bragg’s Law Calculator Calculate diffraction angle or lattice spacing with Bragg’s law for a selected wavelength and order. Boltzmann Factor Calculator Calculate the relative Boltzmann factor for an energy difference at an absolute temperature. Bohr Model Energy and Radius Calculator Estimate a hydrogen-like electron energy level and orbital radius from nuclear charge and principal level. RC Capacitor Charge Time Calculator Calculate the time for a resistor-capacitor circuit to reach a selected percentage of its final charge. Frequency Bandwidth Calculator Calculate bandwidth and center frequency from the lower and upper edges of a frequency band. AC Power and Wattage Calculator Estimate real AC power from voltage, current, power factor, and single- or three-phase selection. Average Impact Force Calculator Estimate average stopping force from vehicle mass, speed, and stopping distance in a simplified energy model. Reflection Angle Calculator Calculate the reflected angle and complementary angle to the surface from an entered angle of incidence. Electric-Field Particle Acceleration Calculator Calculate the acceleration magnitude of a charged particle in a uniform electric field from charge and mass. Coordinated-Turn Bank Angle Calculator Estimate the bank angle for a level coordinated turn from speed, turn radius, and gravitational acceleration. Arrow Speed from Kinetic Energy Calculator Calculate an idealized projectile speed from mass and kinetic energy. Avogadro’s Law Volume Calculator Calculate a new gas volume from an initial volume and the ratio of final to initial amount of gas at constant temperature and pressure. Brinell Hardness Number Calculator Calculate a simplified Brinell hardness number from force, indenter diameter, and indentation diameter. Shaft Angle of Twist Calculator Calculate elastic shaft twist from torque, shaft length, shear modulus, and polar second moment of area. Simply Supported Beam Deflection Calculator Estimate center deflection of a simply supported beam under a center point load using an Euler–Bernoulli elastic model. Average Acceleration Calculator Calculate average acceleration and displacement under constant acceleration from initial velocity, final velocity, and elapsed time. Broad-Crested Weir Flow Calculator Estimate ideal flow over a broad-crested weir from crest width, head, discharge coefficient, and gravity. Altitude Temperature Estimate Estimate temperature at altitude using a supplied sea-level temperature and a linear lapse rate. Simply Supported Beam Reaction Calculator Calculate total load, equal support reactions, and maximum bending moment for a simply supported beam under uniform load. Elevator Apparent Weight Calculator Calculate apparent weight for a person or object in a vertical elevator acceleration scenario. Charles’s Law Gas Volume Calculator Calculate a gas volume after a temperature change at constant pressure using absolute temperatures. Cloud Base Height Estimate Estimate cloud-base height from air temperature, dew point, and a supplied temperature-dew-point lapse approximation. Conductivity to Resistivity Calculator Convert electrical conductivity into resistivity using the reciprocal relation. Compton Wavelength Calculator Calculate a particle’s Compton wavelength from its rest mass using Planck’s constant and the speed of light. Bending Stress Calculator Estimate bending stress from bending moment, distance to the outer fiber, and second moment of area. Centrifugal Force Magnitude Calculator Calculate the frame-dependent outward force magnitude associated with circular motion from mass, speed, and radius. Two-Object Momentum Conservation Calculator Calculate total one-dimensional momentum and the shared velocity after a perfectly inelastic collision. Flow Coefficient of Discharge Calculator Estimate a discharge coefficient from measured flow, opening area, and hydraulic head. Uniform Circular Motion Calculator Calculate tangential speed and centripetal acceleration from radius and period. Brake-Specific Fuel Consumption Calculator Convert a fuel mass flow and delivered engine power into brake-specific fuel consumption. Dripping Faucet Water Loss Calculator Estimate water lost from a dripping faucet over a day or a selected number of days. Household Water Demand Calculator Estimate total household water demand from people, daily per-person use, and a selected number of days. Reusable Bag Break-Even Calculator Compare the purchase cost of reusable bags with disposable-bag cost across a planned number of uses. Cigarette Butt Mass Calculator Estimate the collected mass of cigarette butts from a count and an entered average mass per item. Compost Carbon-Nitrogen Mix Calculator Estimate additional brown material needed to reach a selected brown-to-green mass ratio in a compost mix. Focal Length from Sensor Width and Field of View Calculate approximate focal length from a camera sensor dimension and horizontal field of view. Guitar String Tension Calculator Estimate ideal string tension from unit mass, vibrating length, and target frequency. Ground Sample Distance Calculator Estimate ground sample distance per image pixel from altitude, sensor pixel pitch, and focal length. Hyperfocal Distance Calculator Calculate approximate hyperfocal distance from focal length, f-number, and circle of confusion. Thin-Lens Magnification Calculator Calculate image distance and lateral magnification from focal length and object distance using the thin-lens equation. Source and Load Impedance Matching Calculator Calculate reflection coefficient and voltage transfer for a resistive source and load pair. Ideal Cable Impedance Calculator Calculate ideal characteristic impedance from inductance and capacitance per unit length. Photography Exposure Value Calculator Calculate exposure value at ISO 100 and the adjusted exposure value from f-number, shutter time, and ISO. Rainfall Collection Volume Calculator Estimate rainfall volume collected over an area from rainfall depth and a runoff or collection efficiency. Bleach Solution Dilution Calculator Calculate stock solution volume and added water for a target concentration and final volume. Radioactive Half-Life Age Calculator Estimate elapsed age from a half-life, initial activity or fraction, and remaining activity fraction. Diffusion Coefficient from Displacement Calculator Estimate a diffusion coefficient from root-mean-square displacement, elapsed time, and dimensionality. Electrolysis Mass Calculator Estimate deposited or released mass from current, time, molar mass, electron count, and Faraday's constant. Reversible Entropy Change Calculator Calculate entropy change from reversible heat transfer and absolute temperature. Two-Ion Ionic Strength Calculator Calculate ionic strength for a two-species solution from concentrations and charge numbers. Langmuir Adsorption Isotherm Calculator Calculate adsorbed quantity from maximum capacity, affinity constant, and equilibrium concentration. Chemical Oxygen Demand Concentration Calculator Convert oxygen consumed by a sample into chemical oxygen demand concentration. Angular Velocity from Rotations Calculator Calculate angular velocity and rotations per minute from completed rotations and elapsed time. Archimedes Buoyant Force Calculator Calculate buoyant force and equivalent supported mass from fluid density and displaced volume. Hawking Temperature Estimate Estimate ideal Hawking temperature from a nonrotating black-hole mass. Relative Centrifugal Force Speed Calculator Calculate rotor speed in RPM from relative centrifugal force and rotor radius. Mechanical Energy Calculator Calculate gravitational potential energy, kinetic energy, and their sum from mass, height, and speed. Compressibility and Bulk Modulus Calculator Calculate compressibility and bulk modulus from pressure change, initial volume, and volume change. Fluid Drag Force Calculator Calculate ideal drag force from fluid density, drag coefficient, reference area, and speed. Distance to Horizon Calculator Estimate geometric horizon distance from planetary radius and observer height. Debye Length Calculator Estimate the electrostatic screening length of a dilute electrolyte from temperature, relative permittivity, and ionic strength. Activity Coefficient Calculator Estimate a dimensionless activity coefficient from activity and concentration relative to a one-molar standard state. Calibration Curve Inversion Calculator Convert a measured signal into an estimated quantity using a linear calibration slope and intercept. Cubic Unit Cell Density Calculator Calculate ideal crystal density from unit-cell edge length, atoms per cell, and molar mass. Degree of Unsaturation Calculator Calculate the index of hydrogen deficiency from carbon, hydrogen, nitrogen, and halogen counts. Electron Configuration Calculator Generate a ground-state orbital-filling configuration for an element or ion up to atomic number 118. Pauling Electronegativity Difference Calculator Estimate a bond electronegativity difference from heteronuclear and homonuclear bond energies. Concentration Equilibrium Constant Calculator Calculate a concentration-based equilibrium constant from product and reactant concentrations and stoichiometric coefficients. Gibbs Free Energy Change Calculator Calculate Gibbs free-energy change from enthalpy change, entropy change, and absolute temperature. Michaelis-Menten Rate Calculator Calculate ideal initial enzyme reaction rate from maximum rate, Michaelis constant, and substrate concentration. Mass Concentration to Molarity Calculator Convert a mass concentration and molar mass into molar concentration. Alfvén Velocity Calculator Calculate ideal magnetohydrodynamic Alfvén speed from magnetic field and mass density. Angle of Refraction Calculator Calculate a transmitted ray angle using Snell's law and two refractive indices. Brewster Angle Calculator Calculate the incidence angle for zero reflected p-polarized light at an ideal dielectric interface. Compton Scattering Wavelength Calculator Calculate the ideal Compton wavelength shift and scattered wavelength for a photon angle. Critical Damping Calculator Calculate critical damping, damping ratio, and ideal damping regime for a mass-spring system. Coriolis Acceleration Calculator Estimate horizontal Coriolis acceleration magnitude from speed, latitude, and planetary rotation rate. Cricket Chirp Temperature Estimate Estimate outdoor temperature from cricket chirps per minute using a classic empirical relation. Dry Matter and Water Content Calculator Split a material mass into dry matter and water from a stated dry-matter percentage. Feed Conversion Ratio Calculator Calculate feed conversion ratio from feed consumed and live-mass gain. Fertilizer Application Quantity Calculator Estimate total fertilizer mass and bag count from area, application rate, and package size. Growing Degree Units Calculator Estimate cumulative growing degree units from daily high and low temperatures, a base temperature, and days. Grain Bin Capacity and Mass Calculator Estimate filled cylindrical grain-bin volume and grain mass from dimensions, fill fraction, and bulk density. Bushel to Mass Grain Conversion Calculator Convert a bushel count to estimated mass using an entered commodity-specific mass per bushel. Cat Energy Requirement Estimate Estimate resting and factor-adjusted daily energy from a cat's body mass using a transparent power-law model. Dog Age to Human-Year Estimate Estimate an adult-equivalent human age from dog age using a simple first-year, second-year, and later-year model. Dog Water Intake Planning Estimate Estimate a daily water-planning amount from body mass and a visitor-entered millilitres-per-kilogram rate. Gravitational Acceleration from Mass and Radius Calculator Calculate gravitational acceleration from a spherical body’s mass and radius. Biot Number Calculator Calculate the Biot number from a convection coefficient, characteristic length, and material conductivity. Second-Order Damping Ratio Calculator Calculate natural frequency and damping ratio from mass, damping coefficient, and spring stiffness. Decibel Power Gain Calculator Calculate power gain in decibels from output and input power. Drake Equation Scenario Calculator Multiply supplied astronomical and biological factors into a communicating-civilization scenario estimate. Earth Curvature Drop Approximation Calculator Estimate geometric curvature drop over a supplied surface distance using a spherical Earth approximation. Sensible Enthalpy Change Calculator Calculate a simple enthalpy change from mass, specific heat, and temperature change. Faraday Electrolysis Mass Calculator Estimate deposited mass from current, time, molar mass, electron count, and Faraday’s constant. Gear Ratio and Output Speed Calculator Calculate gear ratio, output speed, and ideal torque multiplication from tooth counts and input speed. Hydraulic Radius Calculator Calculate hydraulic radius from flow cross-sectional area and wetted perimeter. Hydrostatic Pressure Calculator Calculate gauge pressure from fluid density, gravitational acceleration, and depth. Inverse-Square Law Calculator Scale a field or intensity from one distance to another under an inverse-square model. Joule Heating Energy Calculator Calculate resistive heating energy from current, resistance, and time. Knudsen Number Calculator Calculate the ratio of molecular mean free path to a characteristic length. Laser Beam Divergence Calculator Estimate full-angle far-field beam divergence from wavelength and initial beam diameter under a diffraction-limited circular-aperture model. Electric Motor Torque from Power and Speed Calculator Calculate ideal shaft torque from mechanical power and rotational speed. Linear Actuator Force from Pressure Calculator Calculate ideal force from pressure and piston area. Lift Coefficient Calculator Calculate a dimensionless lift coefficient from lift force, fluid density, speed, and reference area. Free-Space Path Loss Calculator Calculate ideal free-space radio path loss from frequency and distance. Ideal Transformer Voltage and Current Calculator Calculate secondary voltage and current from turns ratio and primary values under an ideal transformer model. Buoyant Force and Net Force Calculator Calculate ideal buoyant force and the net vertical force from fluid density, displaced volume, gravity, and object mass. Darcy-Weisbach Head-Loss Calculator Calculate frictional head loss and pressure loss in a pipe from length, diameter, speed, friction factor, density, and gravity. Double-Slit Diffraction Fringe Spacing Calculator Calculate ideal double-slit fringe spacing from wavelength, screen distance, and slit separation. Charge-Carrier Drift Velocity Calculator Calculate charge-carrier drift speed from current, carrier density, carrier charge, and cross-sectional area. Heat-Exchanger Effectiveness from NTU Calculator Calculate counterflow heat-exchanger effectiveness from number of transfer units and heat-capacity ratio. Equivalent Isotropically Radiated Power Calculator Calculate ideal effective isotropic radiated power from transmitter power, antenna gain, and cable loss. Elastic Moduli Relationship Calculator Calculate Young’s modulus and bulk modulus from shear modulus and Poisson’s ratio under isotropic elasticity. Electron Speed from Kinetic Energy Calculator Estimate non-relativistic electron speed from kinetic energy. Axial Elongation Calculator Calculate ideal axial elongation from force, member length, cross-sectional area, and Young’s modulus. Energy-Limited Evaporation Rate Calculator Calculate an ideal evaporation mass rate from supplied heat input and latent heat of vaporization. Diopter and Focal-Length Calculator Convert a positive focal length in millimetres to optical power in diopters and back to metres. Density Altitude Approximation Calculator Estimate density altitude from pressure altitude and outside-air temperature using a standard atmosphere approximation. Differential Pressure Calculator Calculate the signed pressure difference between two supplied pressure readings and its absolute magnitude. Delta-to-Wye Resistor Conversion Calculator Convert three delta-connected resistances into equivalent wye-connected resistances. Electric and Magnetic Field Energy Density Calculator Calculate electric, magnetic, and total field energy density from electric field and magnetic flux density. Excess Electrons from Charge Calculator Calculate the magnitude of excess or missing elementary charges represented by a supplied net charge. Factor of Safety Ratio Calculator Calculate a screening factor-of-safety ratio from an allowable or failure strength and a selected working load. Volumetric Flow Rate from Area and Speed Calculator Calculate volumetric flow rate from a flow cross-sectional area and mean speed. Electrical Mobility Calculator Calculate charge-carrier mobility from drift speed and applied electric field. Full-Wave Bridge Rectifier Output Calculator Estimate peak and average rectified output from AC RMS voltage and two diode drops. Average Force from Impulse Calculator Calculate average force from an impulse and the time interval over which it acts. Projectile Flight Time from Height Calculator Calculate the positive flight time for a projectile launched from a known height with no air resistance. Projectile Maximum Height from Launch Point Calculator Calculate a projectile’s highest vertical position and time to apex from launch conditions. Work from Force, Distance, and Angle Calculator Calculate mechanical work from a constant force, displacement, and included angle. Spring-Mass Oscillation Frequency Calculator Calculate angular frequency, frequency, and period for an ideal mass-spring oscillator. Simple Pendulum Period Calculator Calculate the period and frequency of a small-angle simple pendulum. Centripetal Acceleration Calculator Calculate inward acceleration and angular speed for circular motion from speed and radius. Fluid Continuity Flow Calculator Calculate downstream speed and volumetric flow from two cross-sectional areas and one measured speed. Bernoulli Pressure Change Calculator Calculate downstream ideal-fluid pressure from pressure, speed, height, density, and gravity inputs. Specific Heat from Energy Calculator Calculate specific heat capacity from supplied heat energy, mass, and temperature change. Ideal Gas Density Calculator Calculate ideal-gas density from pressure, molar mass, absolute temperature, and the gas constant. Photon Wavelength from Energy Calculator Calculate photon wavelength from photon energy using Planck’s constant and the speed of light. Optical Lens Power Calculator Calculate optical power in diopters from a thin-lens focal length. Work from Kinetic Energy Change Calculator Calculate net work from mass and initial and final speeds using the work-energy theorem. Thermal Efficiency from Work and Heat Calculator Calculate thermal efficiency and rejected heat from useful work and input heat. Thermal Conduction Resistance Calculator Calculate planar thermal resistance and steady heat-transfer rate through a material slab. Thermal Radiation Power Calculator Calculate idealized radiative power from emissivity, area, and absolute temperature. Electric Field from a Point Charge Calculator Calculate electric-field magnitude and potential from a point charge and distance. Snell’s Law Refraction Angle Calculator Calculate a refracted angle from two refractive indices and an incident angle. Critical Angle Calculator Calculate the critical angle for total internal reflection from a higher-index medium to a lower-index medium. Cube Density from Mass and Side Calculator Calculate the density of a cube from its mass and side length, with the cube volume shown for checking. Darcy’s Law Flow Rate Calculator Estimate porous-medium flow rate from permeability, area, pressure difference, viscosity, and flow length. Darcy Friction Factor from Head Loss Calculator Rearrange the Darcy–Weisbach relation to estimate a dimensionless friction factor from measured head loss and pipe conditions. Froude Number Calculator Calculate the Froude number for a flow or moving body from speed, characteristic length, and gravity. Heat Capacity from Energy and Temperature Change Calculator Calculate the heat capacity of a body from energy transferred and the resulting temperature change. Heat Transfer Coefficient Calculator Estimate a convective heat-transfer coefficient from heat rate, area, and temperature difference. Hydraulic Gradient Calculator Calculate hydraulic gradient from head loss and the flow distance between two points. Lorentz Force Component Calculator Calculate electric and magnetic force components on a moving charge under a stated same-direction component convention. Force Between Parallel Current-Carrying Wires Calculator Calculate the ideal magnetic force between two long parallel current-carrying wires. Mach Number Calculator Calculate Mach number from an object's speed and the local speed of sound. Mechanical Advantage Calculator Calculate ideal mechanical advantage from load force and applied effort force. Newton’s Law of Cooling Calculator Estimate an object's temperature after a time interval using a first-order Newton cooling model. Nusselt Number Calculator Calculate the dimensionless Nusselt number from a heat-transfer coefficient, characteristic length, and thermal conductivity. Physical Pendulum Period Calculator Calculate the small-angle period and frequency of a rigid-body physical pendulum from inertia, mass, pivot distance, and gravity. Pipe Velocity from Flow Rate and Diameter Calculator Calculate mean pipe velocity from volumetric flow rate and circular pipe diameter. Prandtl Number Calculator Calculate the Prandtl number from specific heat, dynamic viscosity, and thermal conductivity. Lensmaker’s Equation Calculator Calculate thin-lens focal length and optical power from refractive indices and the two surface radii. Enzyme Activity from Product Formation Calculator Calculate enzyme activity from the amount of product formed, reaction time, and sample volume. Electrochemical Cell EMF Calculator Calculate the ideal cell electromotive force from cathode and anode reduction potentials. Graham's Law of Effusion Calculator Compare gas effusion or diffusion rates from the molar masses of two gases. Heat of Combustion per Mass Calculator Calculate the energy released per unit mass from a combustion measurement. Isoelectric Point from Adjacent pKa Values Calculator Estimate the isoelectric point from the two pKa values that bracket the neutral zwitterion. Kp from Kc Equilibrium Constant Calculator Convert a concentration-based equilibrium constant to a pressure-based constant for a gas reaction. Born-Landé Lattice Energy Calculator Estimate ionic lattice energy per mole from charges, interionic distance, Madelung constant, and Born exponent. Atmospheric Water-Vapor Mixing Ratio Calculator Calculate the water-vapor mixing ratio from vapor pressure and total atmospheric pressure. Miller Indices from Lattice Intercepts Calculator Convert integer lattice intercepts into the smallest whole-number Miller indices for a crystal plane. Nernst Equation Cell Potential Calculator Calculate nonstandard electrochemical potential from standard potential, temperature, electron count, and reaction quotient. Normality from Molarity Calculator Calculate solution normality and total equivalents from molarity, reaction-equivalent factor, and volume. Osmotic Pressure Calculator Calculate ideal osmotic pressure from solute molarity, van't Hoff factor, and temperature. Percent Ionic Character Calculator Estimate percent ionic character from the electronegativity difference using the Pauling relationship. Gibbs Phase Rule Degrees of Freedom Calculator Calculate degrees of freedom from the number of components, phases, and externally fixed intensive variables. pKa from Ka Calculator Convert an acid dissociation constant into pKa using the base-10 logarithm. Temperature Coefficient Q10 Calculator Calculate the Q10 temperature coefficient from two rates measured at two temperatures. Reaction Quotient from Activities Calculator Calculate a simple reaction quotient from product and reactant activities with explicit stoichiometric exponents. Saponification Value Calculator Calculate milligrams of potassium hydroxide required per gram of oil or fat from a blank and sample titration. Water Hardness as CaCO3 Calculator Convert dissolved calcium and magnesium concentrations into equivalent water hardness as calcium carbonate. Young-Laplace Pressure Calculator Calculate ideal gauge pressure across a spherical liquid interface from surface tension and radius. Moment of Inertia Shape Calculator Calculate mass moment of inertia for common uniform rods, disks, hoops, and rectangular plates about a stated central or end axis. Three-Phase Motor Current Calculator Estimate the line current required by a balanced three-phase motor from output power, voltage, power factor, and efficiency. Sheet-Metal Bend Allowance Calculator Estimate bend allowance and flat-pattern length from bend angle, inside radius, thickness, K-factor, and straight legs. Brake Mean Effective Pressure Calculator Calculate brake mean effective pressure from engine torque, displacement, and two- or four-stroke cycle selection. Engine Airflow CFM Calculator Estimate theoretical engine airflow from displacement, engine speed, volumetric efficiency, and engine cycle. Vertex Distance Power Conversion Calculator Convert an optical power between two vertex planes using the thin-lens vertex-distance relation. Schwarzschild Radius Calculator Calculate the ideal event-horizon radius of a nonrotating, uncharged black hole from its mass. Molar Curie Constant Calculator Estimate the SI molar Curie constant from an effective magnetic moment expressed in Bohr magnetons. Curie-Law Magnetic Susceptibility Calculator Calculate ideal molar magnetic susceptibility from a Curie constant and absolute temperature. Daylight Hours by Latitude Calculator Estimate daylight duration from latitude, day of year, and axial tilt using a simple solar-declination model. Gear Diametral Pitch Calculator Calculate diametral pitch, circular pitch, and metric module from gear teeth and pitch diameter. Flywheel Energy Storage Calculator Estimate usable rotational energy between maximum and minimum flywheel speeds from moment of inertia. Geometric Propeller Pitch Calculator Estimate theoretical propeller pitch from blade angle and the reference radius of the blade section. Four-Wheel-Drive Crawl Ratio Calculator Calculate total low-range crawl ratio from first gear, transfer-case reduction, and final-drive ratio. Barn and Pole Relativity Calculator Explore Lorentz contraction and the relativity-of-simultaneity gap in a pole-and-barn thought experiment. Ideal Electric Dipole Field Calculator Estimate the far-field magnitude and potential of an ideal electric dipole on its axial or equatorial line. Exoplanet Transit Depth Calculator Estimate the fractional and percentage drop in starlight when a planet crosses its star in a central transit. Fresnel Zone Radius Calculator Calculate a radio-link Fresnel-zone radius and diameter at a point between two antennas. Fermi–Dirac Occupation Calculator Estimate the equilibrium occupation probability of an energy state from its energy, Fermi level, and temperature. Hall Coefficient Calculator Calculate Hall coefficient and a one-carrier density estimate from Hall voltage, sample thickness, current, and magnetic field. Harmonic Wave Equation Calculator Evaluate displacement, wave speed, angular frequency, and wave number for a sinusoidal traveling wave. Helical Coil Geometry Calculator Estimate axial length and wire path length for a regular helical coil from diameter, turn count, and pitch. Helmholtz Resonator Frequency Calculator Estimate the resonance frequency of a bottle-like Helmholtz resonator from opening area, cavity volume, neck geometry, and sound speed. RC High-Pass Filter Calculator Calculate cutoff frequency, magnitude gain, gain in decibels, and phase for an ideal first-order RC high-pass filter. Hohmann Transfer Calculator Estimate the two ideal impulse burns and transfer time between two coplanar circular orbits around the same central body. Hubble's Law Calculator Estimate a distant galaxy's recession velocity from distance and an entered Hubble constant. Hydraulic Conductivity Calculator Estimate Darcy discharge from hydraulic conductivity, cross-sectional area, head difference, and flow length. Hydraulic Jump Calculator Estimate sequent depth, depth ratio, and idealized energy loss for a rectangular-channel hydraulic jump. Log Mean Temperature Difference Calculator Calculate the logarithmic mean temperature difference between two streams in a counterflow or parallel-flow heat-exchanger setup. Orifice Flow Rate Calculator Estimate volumetric flow through a sharp-edged orifice from discharge coefficient, area, pressure difference, and fluid density. Poiseuille Flow Calculator Calculate ideal laminar flow through a circular tube from pressure drop, radius, length, and dynamic viscosity. Stokes' Law Drag Calculator Estimate the low-speed viscous drag on a small spherical particle moving through a fluid. Mean Free Path Calculator Estimate the mean distance and mean time between molecular collisions in a dilute ideal gas. Optical Density Calculator Calculate optical density, transmission, and attenuation from incident and transmitted light intensity. Radiation Pressure Calculator Calculate ideal light pressure and force for a perfectly absorbing or perfectly reflecting surface. Net Positive Suction Head Calculator Calculate available net positive suction head from pump suction pressure, fluid vapor pressure, density, and gravity. Pneumatic Cylinder Force Calculator Estimate ideal and efficiency-adjusted push force from air pressure and piston bore diameter. Rocket Specific Impulse Calculator Calculate specific impulse and equivalent exhaust velocity from rocket thrust and propellant mass-flow rate. Atom and Ion Composition Calculator Calculate mass number, neutron count, and electron count from proton count, neutron count, and ionic charge. Boiling Point from Vapor Pressure Calculator Estimate a liquid's boiling temperature at a target pressure with a two-point Clausius–Clapeyron model. Boiling Point at Altitude Calculator Estimate standard-atmosphere pressure and water-like boiling temperature at altitude using a barometric and Clausius–Clapeyron approximation. Chemical Equation Balancer Balance a chemical equation by conserving the elements in the entered reactant and product formulas. Combustion Analysis Empirical Formula Calculator Estimate an empirical formula from measured masses of carbon, hydrogen, oxygen, and nitrogen in a sample. Hydrocarbon Combustion Stoichiometry Calculator Calculate ideal oxygen, carbon-dioxide, and water amounts for complete combustion of a hydrocarbon CxHy. Crude Protein from Nitrogen Calculator Estimate crude protein mass and percentage from measured nitrogen and an entered nitrogen-to-protein factor. Tank Detention Time Calculator Calculate theoretical detention time from effective tank volume and flow rate, with hours and days shown separately. Effective Nuclear Charge Calculator Estimate effective nuclear charge with a transparent, simplified Slater-rule screening scenario. Molar Ratio from Masses Calculator Convert two chemical masses to moles and compare their amount ratio using entered molar masses. Acid–Base Neutralization Volume Calculator Estimate the volume of one acid or base solution required to neutralize another from concentration, volume, and equivalent stoichiometry. Integrated Rate Constant Calculator Calculate a zero-, first-, or second-order rate constant from initial concentration, final concentration, and elapsed time. Serial Dilution Calculator Calculate the final concentration and cumulative dilution from a repeated per-step retained fraction. Total Dissolved Solids Estimate Estimate total dissolved solids from specific conductance with an entered conversion factor and optional local intercept. Vapor Pressure from Temperature Calculator Estimate vapor pressure at a target temperature from a reference pressure and enthalpy of vaporization using Clausius–Clapeyron. First-Order Crossover Frequency Calculator Estimate the transition frequency and time constant of an ideal first-order RC crossover network. Valve Flow Coefficient (Cv) Calculator Estimate liquid flow from a valve flow coefficient, pressure drop, and specific gravity. Sound Level Distance Attenuation Calculator Estimate free-field sound-level change when the distance from a point source changes. Piston Engine Displacement Calculator Calculate swept engine displacement from cylinder bore, stroke, and cylinder count. Friction Coefficient from Force Calculator Estimate a static or kinetic friction coefficient from friction force and normal force. Gay-Lussac Pressure–Temperature Law Calculator Estimate a gas pressure after a temperature change at constant volume and fixed amount of gas. Magnetic Permeability Calculator Calculate absolute and relative magnetic permeability from magnetic flux density and magnetic field strength. Mass–Spring Natural Frequency Calculator Calculate angular frequency, frequency, and period for an ideal undamped mass–spring oscillator. AC Power Factor Calculator Calculate apparent power, power factor, reactive power, and phase angle from real power and RMS voltage/current. Four-Band Resistor Color Code Calculator Decode the nominal resistance and tolerance range of a standard four-band resistor. Resistor Johnson Noise Calculator Estimate ideal Johnson–Nyquist voltage and current noise for a resistor over a selected bandwidth. Sabine Reverberation Time Calculator Estimate room reverberation time from room volume and total equivalent absorption area. Relative Humidity from Dew Point Calculator Estimate relative humidity and vapor-pressure deficit from air temperature and dew-point temperature. Piston Force from Pressure Calculator Calculate ideal force on a circular piston from net pressure and piston diameter. Mean Piston Speed Calculator Calculate mean piston speed from engine stroke and rotational speed. API Gravity and Specific Gravity Calculator Convert petroleum specific gravity at 60 °F into API gravity, or reverse the relation for a transparent planning check. Exhaust Pipe Diameter from Flow Rate Calculator Estimate the circular flow area and internal diameter needed for a chosen volumetric flow and target average gas velocity. Lifetime-Limited Laser Linewidth Calculator Estimate the Fourier-limited linewidth associated with a finite excited-state lifetime and show the corresponding coherence-time scale. Diffraction-Limited Laser Spot Size Calculator Estimate the Airy-disk diameter, radius, and area for a circular aperture or focused beam using wavelength and focal geometry. Magnetic Dipole Moment Calculator Calculate the ideal magnetic dipole moment of a multi-turn current loop from turns, current, and loop area. Magnus-Style Lift Force Calculator Estimate a transverse aerodynamic force using density, speed, reference area, and a supplied lift coefficient for a spinning or curved-flow object. Spherical Mirror Equation Calculator Find image distance, magnification, and mirror curvature from focal length and object distance using the signed mirror convention. Particle Number Density Calculator Calculate the number of particles per volume and the volume represented by a supplied particle count. Porosity and Kozeny–Carman Permeability Estimate Calculate void fraction and an idealized intrinsic permeability estimate from porosity, grain diameter, and a supplied Kozeny constant. Power-to-Weight Ratio Calculator Compare a machine or vehicle's power with its mass in W/kg, kW per metric tonne, and horsepower per metric tonne. Principal Stress and Maximum Shear Calculator Resolve a two-dimensional stress state into principal stresses, maximum in-plane shear stress, and principal-angle orientation. Pulley Mechanical Advantage Calculator Estimate ideal and efficiency-adjusted effort, mechanical advantage, and rope travel for a block-and-tackle style pulley arrangement. Two-Body Recoil Energy Calculator Estimate recoil velocity and kinetic energy from an ideal isolated two-body momentum exchange. Two-Force Resultant Calculator Add two planar force vectors by magnitude and angle, returning Cartesian components, resultant magnitude, and direction. Root-Mean-Square Molecular Speed Calculator Calculate the ideal-gas root-mean-square molecular speed from temperature and molar mass. Signal-to-Noise Ratio Calculator Convert signal and noise power into a linear ratio, decibel value, and percentage noise relative to the signal. Simple Harmonic Motion Position Calculator Evaluate displacement, velocity, and acceleration at a time in ideal sinusoidal motion from amplitude, frequency, and phase. Electromagnetic Skin Depth Calculator Estimate the depth at which a sinusoidal electromagnetic field falls to 1/e in a conductor from frequency, permeability, and conductivity. Sound Absorption Coefficient Calculator Calculate the absorbed energy and normal-incidence absorption coefficient from incident and reflected sound energy. Quadratic-Drag Terminal Velocity Calculator Estimate terminal speed when gravitational force balances quadratic drag in a fluid. Latitude and Longitude Distance Calculator Estimate great-circle distance and initial bearing between two geographic coordinates using a transparent spherical Earth model. Mass Percent of a Solution Calculator Calculate the mass percentage of a solute in a solution and show the corresponding mass fraction and parts-per-million estimate. Molar Mass from Gas Measurements Calculator Estimate a gas sample's molar mass from measured mass, pressure, volume, and absolute temperature using the ideal-gas relation. Protein Solubility Assay Calculator Convert dissolved protein mass and sample volume into soluble concentration, recovery percentage, and undissolved remainder for a transparent assay summary. Radioactive Activity after Half-Lives Calculator Estimate remaining activity, undecayed fraction, decay constant, and activity lost after a chosen elapsed time and half-life. Pellet Resuspension Concentration Planner Estimate final cell concentration and the buffer volume needed to resuspend a pellet to a selected target concentration. Stoichiometric Theoretical Yield Calculator Calculate product moles and mass from a limiting-reactant amount, balanced-equation coefficients, and product molar mass. General Stoichiometric Titration Calculator Calculate an analyte concentration from titrant concentration, measured volumes, and balanced-reaction coefficients beyond the simple 1:1 case. Two-Photon Absorption Rate Calculator Estimate weak-field two-photon absorption events from a cross section, photon flux, and number of absorbing molecules. Water Saturation Vapor Pressure Calculator Estimate saturation vapor pressure over liquid water or ice from temperature using a pressure-adjusted Buck formulation and show the result in common pressure units. Thin-Film Interference Calculator Estimate the optical path difference and nearest constructive or destructive reflection condition for a uniform thin film. Afocal Laser Beam Expander Calculator Calculate ideal beam diameter, angular-divergence ratio, and afocal magnification from two lens focal lengths. Manometer Pressure Difference Calculator Calculate gauge and absolute pressure from a manometer liquid density, column-height difference, gravity, and atmospheric pressure. Two-Body Reduced Mass Calculator Calculate the reduced mass and relative-motion kinetic energy of a two-body system from two masses and their relative speed. Elastic Section Modulus Calculator Calculate second moment of area, elastic section modulus, and simple elastic bending stress for common symmetric cross-sections. Synodic Period Calculator Calculate the time for two orbiting bodies to return to the same relative angular configuration from their orbital periods. Thermal Diffusivity Calculator Calculate thermal diffusivity from thermal conductivity, density, and specific heat capacity. Aircraft Wing Loading Calculator Calculate aircraft wing loading from mass, gravity, and projected wing planform area, with optional customary-unit output. Shear Strain and Stress Calculator Calculate engineering shear strain, angular distortion, and elastic shear stress from lateral displacement, layer height, and shear modulus. Von Mises Stress Calculator Calculate equivalent von Mises stress, yield utilization, and remaining stress margin from three principal stresses. Gauss's Law Flux Calculator Calculate electric flux, enclosed charge, and the ideal spherical-surface electric field using Gauss's law. J-Pole Antenna Dimension Calculator Estimate the wavelength, half-wave radiating section, quarter-wave matching section, and total 3/4-wave J-pole length from frequency. Lumen and Illuminance Calculator Calculate luminous flux from candela and solid angle, then estimate illuminance in lux and foot-candles over an area. Lux to Foot-Candle Converter Convert an illuminance value between lux and foot-candles using the NIST conversion factor. Minute of Angle Target-Size Calculator Convert a minute-of-angle value and viewing distance into the corresponding linear size and angular size in radians. AM Modulation Index Calculator Calculate amplitude-modulation depth, envelope limits, sideband amplitudes, and ideal single-tone AM power ratios. NE555 Astable Frequency Calculator Estimate the oscillation frequency, period, timing intervals, and duty cycle of a standard NE555 astable circuit. Redshift and Blueshift Calculator Calculate spectral redshift or blueshift from rest and observed wavelengths, with a low-redshift velocity approximation and scale factor. Rydberg Equation Calculator Calculate a hydrogen-like spectral transition wavelength, wavenumber, and photon energy from atomic number and energy levels. Solenoid Magnetic Field Calculator Estimate the internal magnetic field, magnetic field strength, and turns-per-length of an ideal long solenoid. Cell and Solution Dilution Calculator Use C₁V₁ = C₂V₂ to find the stock volume, diluent volume, and dilution factor for a target concentration and final volume. CO₂ Grow Room Gas Requirement Calculator Estimate the theoretical CO₂ gas volume, amount, and mass needed to raise a sealed room from one measured ppm level to another at entered temperature and pressure. Grass Seed Quantity Calculator Estimate the base and purchase quantity of grass seed from a rectangular area, a label seeding rate, and an optional allowance for uneven establishment. Mulch Volume and Bag Calculator Calculate mulch volume from a rectangular area and layer depth, then estimate the liters and bags needed after an explicit waste allowance. Plant Population and Row Spacing Calculator Estimate how many planting rows, plants per row, and total planting positions fit inside a rectangular bed using center-to-center spacing. Potting Soil Volume and Bag Calculator Estimate the fill volume for repeated rectangular containers, apply a fill percentage, and round the result to whole bags. Raised Bed Soil Volume Calculator Calculate the soil volume for a rectangular raised bed and estimate bag count after a chosen settling or top-up allowance. Tree Spacing and Hectare Density Calculator Estimate theoretical tree density from row and in-row spacing and scale it to a selected land area without treating the result as a stocking prescription. Vegetable Row Seed Quantity Calculator Estimate seed positions, adjusted seed count, and seed mass for a row using spacing, germination, establishment, and seeds-per-gram inputs. Water-Soluble Fertilizer Mass from ppm Calculator Convert a chosen nutrient target in ppm and solution volume into nutrient mass, product mass from a label percentage, and whole packets. Isotope-Weighted Atomic Mass Calculate an element's average atomic mass from isotope masses and their percentage abundances. Particles, Moles, and Mass Bridge Convert a particle count or mole amount into the corresponding moles, particles, and mass for a supplied molar mass. Mass and Molar Concentration Calculate mass concentration and molar concentration from solute mass, final solution volume, and molar mass. Double Bond Equivalent Calculator Estimate degrees of unsaturation from carbon, hydrogen, nitrogen, and halogen counts in an organic formula. Solution Dilution Factor Calculate how many times a stock solution must be diluted to reach a target concentration and show the final-to-stock fraction. Henderson-Hasselbalch Buffer Calculator Estimate buffer pH from pKa and the conjugate-base-to-acid concentration ratio. Hydrogen-Ion Concentration and pH Convert between pH and hydrogen-ion concentration while showing pOH under the 25 °C dilute-aqueous convention. Precipitation Net-Ionic Equation Builder Build a bounded precipitation net-ionic equation from selected aqueous ions and a supported insoluble product pair. Percent w/v to Molarity Converter Convert grams-per-100-milliliters percentage concentration into molarity using the solute molar mass. Common Chemical Formula Name Lookup Look up the common name and formula class for a bounded set of frequently encountered chemical formulas. Parallel-Plate Capacitance and Stored Energy Estimate the capacitance, charge, stored energy, and electric field of an ideal parallel-plate capacitor. Quadratic Drag Force and Terminal Speed Calculate idealized quadratic drag force and the corresponding terminal speed for an object moving through a fluid. Poisson's Ratio from Axial and Lateral Strain Calculate Poisson's ratio and the dimensional changes of a specimen from signed axial and lateral strains. Mass Moment of Inertia for Common Shapes Calculate the mass moment of inertia about a stated idealized axis for a point mass, rod, hoop, disk, sphere, or cylinder. Normal Force on a Supported Incline Estimate the contact normal force for a mass on an incline with an optional force directed away from or toward the surface. Circular Orbital Period Calculate the period, circular speed, and local gravitational acceleration for an ideal circular orbit around a central mass. Laminar Pipe Flow by Hagen–Poiseuille Estimate flow rate, mean speed, and Reynolds number for a pressure-driven Newtonian fluid in a circular pipe. One-Dimensional Impulse and Momentum Calculate initial and final momentum, impulse, average force, and kinetic-energy change from a one-dimensional velocity change. Drake Equation Civilization Estimate Estimate the number of detectable technological civilizations from the seven factors in the Drake equation. Binoculars Angular-Size Range Estimate the distance to a target of known height from its apparent angular size and binocular magnification. Vehicle Center of Mass from Axle Loads Estimate a vehicle's longitudinal center of mass from front and rear axle loads and wheelbase. Elevated Vehicle Jump Distance Estimate flight time, horizontal distance, and impact speed for an ideal projectile launched from an elevated ramp. Ideal Constant-Acceleration Interstellar Travel Estimate one-way travel time for a symmetric accelerate–cruise–decelerate journey to a stated distance. Light Frequency from Wavelength Calculate electromagnetic-wave frequency, period, photon energy, and wavenumber from wavelength in vacuum. Fulcrum Lever Balance Find the effort force, mechanical advantage, and ideal pivot reaction for a two-force lever in static balance. Schwarzschild Gravitational Time Dilation Estimate the proper time elapsed near a spherical nonrotating mass compared with a distant coordinate-time interval. Hair-Width Diffraction Estimate Estimate the first diffraction minimum angle and screen displacement for light diffracted by an opaque hair-sized obstacle. Hydrogen-Like Atom Energy Transition Calculate Bohr-model energy levels, orbit radii, and photon wavelength for a one-electron ion transition. Lightning Distance from Thunder Delay Estimate how far away a lightning flash was from the time between seeing the flash and hearing thunder. Radar Horizon Range Estimate the geometric line-of-sight range to a target from radar antenna height, target height, and an effective Earth radius. Luminosity from Flux and Distance Calculate a source's total radiated power from measured energy flux and distance using the inverse-square relationship. Quantum Number Validity and Orbital Capacity Check a set of electron quantum numbers and calculate its shell, subshell, orbital, and electron capacities. Poise and Stokes Viscosity Converter Convert dynamic viscosity to SI and poise units and derive kinematic viscosity in stokes from density. 3D Acceleration Magnitude Find the total acceleration magnitude and g-equivalent from perpendicular x, y, and z acceleration components. Aircraft Ground Speed with Wind Vector Calculate an aircraft's ground speed and track from airspeed, heading, and meteorological wind direction and speed. Foot-Pounds of Work and Energy Calculate mechanical work in foot-pounds-force from a force, distance, and included angle, then convert it to joules. Laser Beam Irradiance Estimate optical power density from laser power and circular spot diameter, with watts per square metre and decibel output. Coefficient of Performance Calculate a heating or cooling system's coefficient of performance from useful output energy and supplied input energy. Cube-Root Blast-Scaling Radius Scale a reference blast-effect radius to a different TNT-equivalent yield with the cube-root scaling relationship. Capacitive Transformerless Supply Sizing Estimate capacitive reactance, reactive VA, and series-capacitor value for a target RMS current at a stated AC voltage and frequency. Mass from Density and Volume Calculate an object's mass from its density and volume while returning the SI volume and specific-volume equivalents. Free Fall with Quadratic Air Resistance Estimate fall time, final speed, and terminal speed for an object dropped from rest under a constant quadratic-drag model. Root-Mean-Square Molecular Speed Calculate the root-mean-square speed of ideal-gas molecules from temperature and molar mass. Sound Wavelength from Speed and Frequency Calculate a sound wave's wavelength and period from its propagation speed and frequency. Surface Tension from Force and Length Calculate surface tension from a measured force acting along a liquid-surface length. van der Waals Gas Pressure Calculate non-ideal gas pressure from amount, temperature, volume, and van der Waals constants. Vickers Hardness Number Calculate Vickers hardness from indentation load and the two measured diagonals of a square-pyramidal diamond impression. Energy to TNT Equivalent Convert an energy value in joules to an equivalent mass of TNT using the standard energy-equivalence factor. Specific Gas Constant Calculate a gas's specific gas constant from its molar mass using the universal molar gas constant. Wavenumber from Wavelength Calculate spatial wavenumber, cycles per metre, and frequency from wavelength and propagation speed. Wind Correction Angle Solve the horizontal wind triangle for a heading correction, groundspeed, and crosswind components along a chosen course. Wheatstone Bridge Balance Calculate the unknown resistance at balance and the detector voltage for a four-resistor Wheatstone bridge. Apparent Power in kVA Calculate single-phase or balanced three-phase apparent power, real power, and reactive power from RMS voltage, current, and power factor. Voltage Regulation Calculate voltage regulation from no-load and full-load output voltage and show the resulting load drop. Young's Modulus from Stress and Strain Calculate tensile or compressive Young's modulus from force, cross-sectional area, original length, and extension. RMS Voltage for a Sine Wave Convert sinusoidal peak voltage to RMS, peak-to-peak, average-rectified voltage, and resistive-load power. Water Pressure at Depth Calculate gauge and absolute hydrostatic pressure below a fluid surface from depth, density, surface pressure, and gravity. Telescope Field of View Estimate telescope magnification, true angular field of view, and exit pupil from telescope and eyepiece specifications. Horsepower to Amps Estimate motor input current from mechanical horsepower, voltage, phase, power factor, and efficiency. Open-Channel Flow (Manning Equation) Estimate uniform flow velocity and discharge in a rectangular open channel from geometry, slope, and Manning roughness. Speed of Sound in a Solid Estimate longitudinal sound speed in a solid from Young's modulus and density, then calculate travel time over a path. Solar Elevation and Azimuth Angle Calculate the Sun's elevation, zenith, and compass azimuth from latitude, solar declination, and hour angle. Sunrise and Sunset from Solar Geometry Estimate sunrise, sunset, daylight duration, and solar noon from latitude, declination, longitude, time zone, and equation of time. True Airspeed from Equivalent Airspeed Estimate true airspeed from equivalent airspeed and actual air density using the density-ratio relationship. Water Dynamic Viscosity by Temperature Estimate liquid-water dynamic viscosity from temperature using a compact atmospheric-pressure correlation. Watt-Hours from Power and Time Calculate energy use in watt-hours, kilowatt-hours, and joules from power, runtime, quantity, and efficiency. Wave Velocity from Wavelength and Frequency Calculate wave speed, period, and angular frequency from wavelength and ordinary frequency. Wet-Bulb Temperature Estimate wet-bulb temperature from air temperature and relative humidity with the published Stull approximation. Vertical Exaggeration Calculate the vertical exaggeration of a profile from its horizontal and vertical map scales. Microbial Log Reduction Convert initial and surviving organism counts into log reduction, remaining fraction, and percent reduction. qPCR Amplification Efficiency Convert the slope of a qPCR standard curve into amplification efficiency and fold amplification per cycle. Mutation Frequency from Counts Calculate the observed fraction of mutant cells or organisms and express it as a percent or per-million frequency. Plant Water Potential Estimate solute potential from molarity, van't Hoff factor, and temperature, then combine solute, pressure, and gravitational terms. Tree Height from Clinometer Angles Estimate tree height from horizontal distance, top and base sight angles, and observer eye height. Wire Resistance from Resistivity Calculator Calculate the resistance of a uniform conductor from material resistivity, length, and cross-sectional area. VSWR and Return Loss Calculator Convert a reflection-coefficient magnitude into voltage standing-wave ratio, return loss, and reflected power. Stopping Distance Calculator Estimate reaction distance, braking distance, and total stopping distance from speed, reaction time, and deceleration. Inclined-Plane Force Calculator Estimate normal force, downhill gravity, kinetic friction, and the force needed to move an object up an incline at constant speed. LED Series Resistor Calculator Choose a current-limiting resistor for one or more LEDs in series and estimate the resistor voltage and power. Darcy–Weisbach Pipe Friction Loss Calculator Estimate pipe friction head loss and pressure loss from the Darcy friction factor, length, diameter, velocity, and fluid density. Air Kinematic Viscosity Calculator Calculate air kinematic viscosity from dynamic viscosity and density, with a convenient centistokes conversion. Polar Moment of Area Calculator Find the polar second moment of area for a solid circular shaft or an annular tube and show its torsional section modulus. Pump Horsepower Calculator Estimate hydraulic and brake horsepower from pump flow, head, specific gravity, and pump efficiency. Resultant Velocity Calculator Combine perpendicular velocity components to find resultant speed, horizontal direction, and elevation angle. Ripple Capacitor Size Calculator Estimate the minimum bulk capacitance needed for a switching-converter ripple limit while exposing the ESR contribution. Ideal Flyback Converter Calculator Estimate flyback output voltage and the duty cycle needed for a target from input voltage, turns ratio, and diode drop. Ideal Forward Converter Calculator Estimate forward-converter output voltage and target duty cycle from input voltage, transformer turns ratio, and diode drop. Decibel Ratio Calculator Convert a positive measured-to-reference power or amplitude ratio into decibels and percentage change. Kinematic Displacement Calculator Calculate one-dimensional displacement, final position, final velocity, and average velocity under constant acceleration. Cylinder Density Calculator Calculate the volume and density of a uniform solid cylinder from its mass, diameter, and height. Magnetic Declination Bearing Correction Calculator Convert a magnetic bearing to a true bearing using a supplied local magnetic declination value. Circular Orbit Period and Speed Calculator Estimate circular-orbit period, speed, and local escape speed from central mass and orbital radius. Electric Dipole Moment Calculator Calculate the magnitude of an electric dipole moment from separated charge and charge-center distance. Relativistic Length Contraction Calculator Calculate the length observed parallel to motion when an object travels at a chosen fraction of light speed. Rocket Engine Thrust Calculator Estimate rocket thrust from exhaust mass flow, exhaust velocity, nozzle area, and exit-to-ambient pressure difference. Marine Propeller Slip Calculator Estimate apparent propeller slip from engine speed, gear ratio, propeller pitch, and measured boat speed. Fully Restrained Thermal Stress Calculator Estimate axial thermal stress, thermal strain, and free expansion for a linearly elastic member that cannot expand. Virtual Temperature Calculator Estimate meteorological virtual temperature from air temperature and water-vapor mixing ratio. CFD y⁺ Wall-Distance Calculator Calculate dimensionless wall distance y⁺ from first-cell distance, friction velocity, and kinematic viscosity. Density from Mass and Volume Calculator Calculate density and specific volume from a mass and volume measured on the same unit basis. Electrical Power Calculator Estimate real power, apparent power, energy, and resistance from voltage, current, power factor, and operating time. Frequency to Wavelength Calculator Convert frequency and wave speed into wavelength, period, and wavenumber for a stated medium or signal. Rolling Resistance Force and Power Calculator Estimate level-road rolling-resistance force, power, and work from mass, coefficient, speed, and distance. Column Slenderness Ratio Calculator Calculate effective length and KL/r slenderness ratio from unsupported length, effective-length factor, and radius of gyration. Reaction Time Distance Calculator Estimate distance traveled during a stated reaction time at a stated speed. Speed of Sound in Dry Air Calculator Estimate the speed of sound in dry air from temperature using a stated near-room-temperature approximation. Moisture Content Wet and Dry Basis Calculator Calculate water mass and moisture content on wet and dry bases from wet and dry sample masses. Gold Volume to Weight Estimate Calculator Estimate pure-gold mass equivalent and troy ounces from volume and an entered purity percentage. Generator Useful Power Calculator Estimate useful real output and energy from a generator apparent-power rating, power factor, efficiency, and operating time. Supersonic Isentropic Flow Calculator Calculate ideal supersonic flow ratios, critical-area ratio, Mach angle, and Prandtl-Meyer angle from Mach number and heat-capacity ratio. Weak Oblique Shock Calculator Estimate weak attached-shock angle and downstream flow ratios from upstream Mach number, turning angle, and specific-heat ratio. Prandtl-Meyer Expansion Calculator Calculate downstream Mach number and ideal pressure, temperature, and density ratios through a supersonic expansion fan. Shear-Wave Velocity Calculator Estimate shear-wave speed in a material from shear modulus and density, with an optional travel-time scenario. Thermal Conductivity Heat-Flow Calculator Estimate steady one-dimensional conductive heat flow through a slab from conductivity, area, thickness, and temperature difference. Rotational Stiffness Calculator Estimate a linear torsional stiffness and ideal elastic energy from applied torque and angular displacement. Spherical Capacitor Calculator Calculate ideal capacitance and stored energy for two concentric spherical conductors with a specified dielectric. Intrinsic Semiconductor Carrier Concentration Calculator Estimate equilibrium intrinsic carrier concentration from effective density of states, band gap, and temperature. Mixed Air Temperature Calculator Calculate the ideal adiabatic mixed-air temperature from two mass-flow streams, temperatures, and specific heats. Frequency and Period Calculator Calculate frequency, period, angular frequency, and a wavelength-based wave speed from a counted cycle interval. Sensible Heat Calculator Calculate the energy needed to change a sample temperature from its mass, specific heat capacity, and temperature interval. Spring Rate and Natural Frequency Calculator Estimate linear spring rate, stored elastic energy, and ideal small-oscillation frequency from force and deflection. Stress Concentration Factor Calculator Estimate an elastic local peak stress and a simple allowable-stress ratio from nominal stress and an entered Kt factor. Twist Rate Calculator Convert a signed number of revolutions over a length into turns per metre, radians per metre, degrees per millimetre, and pitch. Thrust-to-Weight Ratio Calculator Calculate thrust-to-weight ratio, excess thrust, and an ideal no-drag vertical acceleration estimate from force inputs. Age on Other Planets Calculator Convert an Earth age into planetary years and completed birthdays using the selected planet’s sidereal orbital period. Steady Conduction Heat Transfer Calculator Estimate steady heat-transfer rate and energy through a flat layer from conductivity, area, temperature difference, thickness, and time. Telescope Magnification and Exit Pupil Calculator Calculate visual telescope magnification, exit pupil, and focal ratio from objective and eyepiece dimensions. Preliminary Wind Load Force Calculator Estimate dynamic wind pressure and a drag-based force from air density, wind speed, exposed area, drag coefficient, and an optional exposure factor. Solid Shaft Torsional Size Calculator Estimate the required diameter and torque capacity of a solid circular shaft from torque, allowable shear stress, and a safety factor. Enhancement MOSFET Operating Point Calculator Estimate an ideal n-channel enhancement MOSFET current, region, transconductance, and drain power from the square-law model. BJT Voltage-Divider Bias Calculator Estimate the base, collector, and emitter currents and the Q-point of an NPN transistor using a voltage-divider bias model. Single-Phase Motor Power-Factor Capacitor Calculator Estimate the shunt capacitor needed to move a single-phase inductive load from an entered power factor to a higher target. Ideal-Gas Thermodynamic Process Calculator Compare final state, boundary work, internal-energy change, and heat transfer for an ideal-gas isothermal, isobaric, isochoric, or adiabatic process. True Strain Calculator Calculate logarithmic true strain, engineering strain, stretch ratio, and percentage change from original and final lengths. Shear Modulus from Stress and Strain Calculator Calculate an apparent shear modulus from entered shear stress and dimensionless shear strain. Muzzle Velocity from Projectile Energy Calculator Calculate the ideal exit speed of a projectile or object from its mass and kinetic energy, with momentum and unit conversions shown. kVA to Amperage Calculator Convert apparent power, RMS voltage, and single- or balanced three-phase selection into an estimated line current. MOSFET Threshold Voltage from Operating Point Calculator Estimate an ideal n-channel MOSFET threshold voltage from a measured or specified drain current, square-law parameter, and gate-to-source voltage. AWG Wire Gauge Geometry and Resistance Calculator Convert an American Wire Gauge number into conductor diameter, cross-sectional area, and estimated resistance for a selected material and length. Volts to Electron-Volts Energy Calculator Calculate the energy change in electron-volts and joules from a potential difference and a charge expressed in elementary-charge units. Latitude and Longitude to UTM Converter Convert WGS84 latitude and longitude into a Universal Transverse Mercator zone, latitude band, easting, and northing for locations between 80°S and 84°N. Psychrometric Moist-Air Properties Calculator Estimate saturation pressure, vapor pressure, humidity ratio, dew point, specific volume, and moist-air enthalpy from dry-bulb temperature, relative humidity, and air pressure. Spring Rate Unit Converter Convert a spring stiffness value between newtons per metre, newtons per millimetre, pound-force per inch or foot, kilopounds per inch, kilogram-force per millimetre, and equivalent joules per square metre. Pure Water Density by Temperature Calculator Estimate pure-water density at atmospheric pressure from temperature, then calculate the mass of a chosen water volume and compare an object's density with the water state. Rolling Cylinder Ramp Race Calculator Compare the ideal acceleration, final speed, and travel time of a solid cylinder, cylindrical tube, or thin shell rolling down a ramp from rest. Quarter-Mile Performance Estimate Estimate quarter-mile elapsed time and trap speed from vehicle mass, engine power, and a selected empirical drag-racing correlation, with metric and imperial inputs supported. Water Heating Energy and Time Calculator Estimate the sensible energy, input energy, and heating time for a stated mass of liquid water when the heater power and efficiency are known. Refrigeration Ton to Kilowatt Converter Convert refrigeration capacity in tons of cooling into kilowatts and British thermal units per hour without confusing cooling capacity with electrical input power. SiPM Photon Detection Efficiency Calculator Estimate photon detection efficiency from responsivity, wavelength, gain, optical crosstalk, and afterpulsing using a transparent SiPM measurement relation. Relativistic Bug–Rivet Paradox Calculator Explore length contraction, information-travel time, tip travel, and critical speed ratios in a bounded educational bug–rivet thought experiment. Universe Expansion Scenario Model Integrate a bounded dimensionless scale-factor scenario from present time using matter, radiation, curvature, dark-energy fractions, and a chosen Hubble constant. Actual and Theoretical Yield Calculator Calculate percent yield and the difference between theoretical and recovered product mass from an explicit chemistry experiment. Standard Temperature and Pressure Gas Calculator Compare common standard-state conventions by calculating ideal-gas volume, mass, density, and molar volume for a chosen amount of gas. Newton’s Third-Law Force Pair Calculator Resolve one interaction force into components and return the equal, opposite force on the other body without confusing the pair with forces on one body. SUVAT Constant-Acceleration Calculator Calculate final velocity, displacement, final position, and average velocity for one-dimensional motion with constant acceleration. CNC Machining Speeds and Feeds Calculator Estimate spindle speed and feed rate from cutting speed, tool diameter, flute count, chip load, and a user-entered machine RPM limit. Circular Shaft Torsional Constant Calculator Calculate the polar torsional constant, elastic torsional stiffness, twist, and surface shear stress for a solid circular shaft. Torsional Spring Torque and Energy Calculator Calculate elastic torque, total torque with an entered preload, angular deflection, and stored spring energy for an ideal torsional spring. Rockwell C and Vickers Hardness Estimate Estimate a Rockwell C or Vickers hardness value for the ASTM non-austenitic-steel equation scope, with the material and validity limits kept visible. Earthquake Magnitude and Energy Scenario Calculator Estimate the approximate energy associated with a moment magnitude and compare the energy and amplitude ratios between two magnitudes. Corrosion Thickness-Loss Scenario Calculator Estimate linear material thickness loss from an entered corrosion penetration rate and test how long a component remains above a chosen minimum thickness. Vapor Pressure Deficit Calculator Estimate saturation vapor pressure, actual vapor pressure, and vapor pressure deficit from air temperature and relative humidity using a transparent FAO-style approximation. Horse Weight Estimate Calculator Estimate a horse's body weight from heart-girth circumference and body length using a clearly labeled measurement-based equation and life-stage divisor. Tree Diameter from Circumference Calculator Convert a measured tree circumference into diameter, radius, and common forestry units while keeping the measurement height visible. Tree Age Growth-Factor Estimate Estimate a tree's approximate age from diameter and a user-selected growth factor, with a visible uncertainty band rather than a false exact age. Vegetable Yield Planning Calculator Estimate a garden harvest from growing area, an entered yield density, and the number of planned harvest cycles without pretending every crop or climate has one fixed yield. Trihybrid Cross Probability Calculator Calculate the eight dominant and recessive phenotype probabilities for three independently assorting traits from six parent genotype inputs. Protein Molecular Weight from Sequence Calculator Estimate a protein's average molecular mass from a one-letter amino-acid sequence, accounting for peptide-bond water loss and reporting daltons and kilodaltons. MLVSS Wastewater Solids Calculator Calculate mixed-liquor volatile suspended solids concentration, inert suspended solids, and total volatile solids mass from MLSS, volatile fraction, and basin volume. Horse Gestation Date Range Calculator Estimate average, early-bound, and late-bound foaling dates from a breeding date and explicit horse gestation intervals. Engine Compression Ratio Calculator Calculate swept displacement, total cylinder volume, and nominal static compression ratio from bore, stroke, cylinder count, and clearance volume. Simplified Circuit Breaker Load Estimate Estimate a planning minimum overcurrent-device rating from continuous and noncontinuous loads, then round to a common standard rating. Light-Year Distance and Travel-Time Converter Convert a distance in light-years to metres, kilometres, astronomical units, parsecs, and the corresponding light-travel time. Current-Loop Magnetic Dipole Moment Calculator Calculate the magnetic dipole moment of a multi-turn current loop and its ideal torque and potential energy in a uniform magnetic field. Circular Shaft Torsional Stiffness Calculator Estimate the torsional stiffness, twist torque, and outer-fiber shear stress of a circular shaft from material rigidity and geometry. Watts to Lux Estimate from Luminous Efficacy Estimate illuminance from electrical power, a supplied luminous efficacy, utilization factor, and illuminated area. Buoyancy Experiment Density Calculator Use mass readings in air and while fully submerged to estimate apparent mass loss, buoyant force, displaced volume, and object density. Pendulum Kinetic Energy Calculator Estimate height drop, ideal speed, potential-energy loss, and kinetic-energy gain for a pendulum released from rest at one angle. Earth Curvature Geometry Comparator Compare the exact spherical-surface drop below a local tangent plane with the small-distance approximation and a flat-plane zero-drop reference. Capillary-Tube Pressure-Drop Screening Calculator Estimate single-phase frictional pressure drop, Reynolds number, velocity, and head loss in a small tube from flow, fluid properties, length, diameter, and roughness. Smartphone Projector Lens Geometry Calculator Estimate screen distance, signed magnification, projected image height, and orientation from a thin-lens smartphone projector geometry. Lever Mechanical Advantage Calculator Estimate ideal and efficiency-adjusted mechanical advantage, output force, and work for a simple lever. Sphere Density from Mass and Diameter Calculate the volume, average density, weight, and specific gravity of an ideal sphere from mass and diameter. Air Water-Vapor Mixing Ratio Calculator Calculate water-vapor mixing ratio, mass fractions, and dry-air pressure from vapor and total pressure. Control-Valve Cv Requirement Calculator Compare required and rated liquid valve Cv from target flow, pressure drop, and specific gravity. Impact Test Energy Screening Calculator Estimate impact energy, absorbed energy, average stopping force, momentum, and area-normalized energy in a simplified test scenario. Grams to Moles Chemistry Calculator Convert a measured mass and a supplied molar mass into moles, millimoles, and an estimated count of specified entities. Molecular Weight from Chemical Formula Calculator Parse a chemical formula with element counts and brackets to estimate molar mass, relative molecular mass, and total atoms per formula unit. Moles to Atoms Calculator Convert moles of molecules, formula units, or another specified entity into entity count, individual atom count, and moles of atoms. Percent Solution Concentration Calculator Calculate w/w, w/v, or v/v solution concentration from a solute amount and the total solution amount using matching basis units. Solution Dilution Calculator Use C₁V₁ = C₂V₂ to check an entered stock volume, calculate the stock volume needed for a target concentration, and find the diluent volume. Elliptical Impact Angle Estimator Estimate an acute angle from the measured major and minor axes of an ellipse-shaped impact mark, with explicit forensic limitations. Hardy–Weinberg Equilibrium Calculator Estimate allele frequencies, expected two-allele genotype counts, and a chi-square screening value from observed genotype counts. Projectile Kinetic Energy Calculator Calculate classical kinetic energy and momentum from projectile mass, speed, and a stated count for an educational physics worksheet. DC Resistor Wattage Calculator Solve a single-resistor DC circuit from any selected pair of voltage, current, and resistance values, then show dissipated power and a visible planning margin. Kilograms to Newtons (Mass to Weight) Calculator Convert a mass into gravitational force using an explicitly entered local gravitational acceleration. Normal Stress Calculator Calculate average axial normal stress from an applied force and loaded cross-sectional area. Capacitor Charge and Energy Calculator Calculate stored charge and electrostatic energy from capacitance and voltage for an ideal capacitor. Vertical Rope Tension Calculator Estimate the tension in an ideal vertical rope supporting a mass with a stated vertical acceleration. Ohm's Law Current Calculator Calculate current through an ideal ohmic resistance from voltage and resistance, with power and conductance shown as supporting results. Average Shear Stress Calculator Calculate average shear stress from a shear force and resisting area, with Pa, kPa, and MPa outputs. Wattage to Amperage Calculator Estimate electrical current from real power, voltage, and power factor for a single-phase or balanced three-phase model. Horizontal Projectile Motion Calculator Calculate flight time, horizontal range, and impact speed for an object launched horizontally from a height. Local Sidereal Time Calculator Calculate Julian date, approximate Greenwich mean sidereal time, and local mean sidereal time from a UTC date, time, and longitude. Rain-to-Snow Equivalent Calculator Estimate fresh and settled snow depth from liquid-equivalent precipitation, a chosen snow-to-liquid ratio, and a transparent settling allowance. Flight Cosmic-Radiation Exposure Estimate Estimate cumulative effective dose from an entered average in-flight dose rate, flight duration, number of flights, and optional scenario reduction. Cat Age to Human-Equivalent Years Calculator Estimate a cat's human-equivalent age from completed years and months using a transparent staged age convention and an explicit life-stage band. Cat Pregnancy Date-Range Calculator Estimate early, typical, and late planning dates from a cat breeding or ovulation reference date and editable gestation intervals. Bird Age to Human-Equivalent Years Calculator Map a bird's chronological age onto a user-supplied human reference lifespan while keeping the species lifespan assumption visible. Protein Concentration from A280 Calculator Estimate protein concentration from a corrected 280 nm absorbance, path length, dilution factor, and protein-specific 0.1% extinction coefficient. Wastewater Flow Planning Calculator Estimate average flow, infiltration and inflow allowance, peak design flow, and a simple retention volume from population and entered planning assumptions. Saturated Liquid Ethylene Density Calculator Interpolate a NIST table of saturated-liquid ethylene molar density from 105 K to 160 K and convert it to an approximate mass density. BTU per Hour to Refrigeration Tons Calculator Convert cooling capacity in BTU per hour to refrigeration tons, kilowatts, and daily heat-removal equivalents. Specific Gravity from Density Calculator Calculate specific gravity from a material density and an explicit reference density, with a sample-mass comparison. Particle Speed from Kinetic Energy Calculator Solve the classical non-relativistic kinetic-energy equation for particle speed and momentum from energy and mass. Two-Node Spring Stiffness Matrix Calculator Build the local 2×2 stiffness matrix for a linear spring element and calculate nodal forces, extension, and strain energy. Moist-Air Mixing Calculator Estimate the mixed dry-bulb temperature, humidity ratio, enthalpy, and relative humidity for two adiabatically mixed air streams. Olbers’ Paradox Finite Shell Demonstration Estimate the finite shell contribution and cumulative flux in a simplified uniform-star model to explore why an infinite static universe creates a paradox. Weight on Planets and the Moon How much a mass weighs under each body's surface gravity, in newtons. Friction Force Coulomb friction force from coefficient μ and normal force. Hydraulic Pressure Pressure from an applied force over a piston area, in pascals and kilopascals. Half-Life Remaining Quantity What remains of a decaying sample after a given elapsed time. Percent Concentration (w/w, w/v) Weight/weight or weight/volume percent from solute and total solution. Gas Volume at STP Litres and molecule count for moles of ideal gas at STP. Punnett Square (Single Trait) Offspring genotype odds for a one-gene cross of two parents. Microscope Magnification Total magnification from ocular and objective lenses. CFU per mL (Plate Count) Viable concentration from colonies, plated volume, and dilution. Average Speed Mean travel speed from distance and time, in km/h and m/s. Energy Efficiency Energy efficiency from useful output over total input. Molar Mass Molar mass of a formula with per-element mass breakdown. Buffer pH Buffer pH from pKa and base/acid concentrations. Cell Size from Field of View Mean cell size from microscope field diameter and cell count. Pascal's Hydraulic Lift Output force from input force and two piston areas. Impulse and Momentum Change Impulse, velocity change, and final velocity from force and time. Logistic Population Growth Capped growth from carrying capacity and intrinsic rate. Percent Composition Molar mass and element mass percents from a formula. Decibel Level Comparison Converts an intensity ratio into decibels relative to a reference. Mole Fraction Calculate one component's mole fraction and percentage from its amount and the total amount of substance. Partial Pressure Calculate a component gas's partial pressure from total pressure and its mole fraction. Gibbs Free Energy Change Estimate Gibbs free-energy change from enthalpy change, temperature, and entropy change. Moles to Particles Convert an amount in moles to an estimated number of representative particles using Avogadro's constant. Centripetal Force Calculate the inward radial force needed for an object moving at a stated speed along a circular path. Buoyant Force Calculate the upward buoyant-force magnitude from fluid density, displaced volume, and local gravitational acceleration. Photon Energy Calculate photon energy from wavelength using Planck's constant and the speed of light. Activation Energy from Two Rates Estimate an apparent activation energy from two rate constants measured at different absolute temperatures. Air-Fuel Ratio Calculate the mass ratio of air to fuel and its reciprocal fuel-to-air ratio for a stated mixture. Alligation Mixture Find the masses of a low-concentration and high-concentration material needed to make a target concentration. Arrhenius Equation Estimate a rate constant from a pre-exponential factor, activation energy, and absolute temperature. Atom Economy Calculate the theoretical percentage of reactant mass incorporated into a desired product. Beer-Lambert Law Calculate absorbance, transmittance, and percent transmittance from molar absorptivity, path length, and concentration. Boiling-Point Elevation Estimate the boiling-point increase caused by a dissolved solute using molality and the solvent constant. Molecular-Orbital Bond Order Calculate a simple molecular-orbital bond order from bonding and antibonding electron counts. Weighted Average Atomic Mass Calculate the weighted average mass of a two-isotope mixture from isotope masses and percentage abundances. Weak-Acid Buffer Capacity Estimate the buffer capacity of a monoprotic weak-acid system from total concentration, pKa, and pH. de Broglie Wavelength Calculate the matter-wave wavelength associated with a supplied particle momentum. Electric Field of a Point Charge Calculate the electric-field magnitude at a distance from an ideal point charge in vacuum. Electric Potential of a Point Charge Calculate the electric potential at a distance from an ideal point charge. Magnetic Field of a Straight Current-Carrying Wire Calculate the magnetic-field magnitude around an ideal long straight wire carrying current. Simple Pendulum Frequency Estimate the oscillation frequency of an ideal simple pendulum from its length and local gravity. Ideal LC Resonant Frequency Calculate the natural resonant frequency of an ideal inductor-capacitor circuit. Ideal Rocket Delta-v Estimate ideal rocket velocity change from specific impulse and initial and final mass. Photoelectric Effect Calculate the maximum photoelectron kinetic energy from wavelength and a material work function. Allele Frequency Calculate the frequencies of two alleles from their observed copy counts in a population sample. Daily Light Integral Estimate daily photosynthetic photon delivery from average PPFD and illuminated hours. DNA to mRNA Sequence Transcribe a DNA sequence into an mRNA sequence using an explicit coding or template strand choice. Capacitive Reactance Calculate the magnitude of a capacitor's opposition to sinusoidal AC at a chosen frequency. Inductive Reactance Calculate the magnitude of an inductor's opposition to sinusoidal AC at a chosen frequency. Capacitor Stored Energy Calculate the ideal energy and charge stored by a capacitor at a supplied voltage. Capacitors in Series Find the equivalent capacitance of two or more ideal capacitors connected in series. Parallel Capacitors Find the equivalent capacitance of two or more ideal capacitors connected in parallel. Inductors in Series Find the equivalent inductance of two or more ideal uncoupled inductors connected in series. Inductors in Parallel Find the equivalent inductance of two or more ideal uncoupled inductors connected in parallel. Current Divider Calculate the currents in two parallel resistive branches from total current and branch resistances. Voltage Divider Calculate the output voltage and current of an unloaded two-resistor series divider. RC Circuit Charging Estimate capacitor voltage, charge, and current during ideal charging from a constant-voltage step. Series RLC Impedance Calculate the magnitude, net reactance, and phase angle of an ideal series RLC circuit at one frequency. Source Internal Resistance Calculate terminal voltage and power losses for an ideal source with internal resistance delivering current. Acres Per Hour Calculate an area-completion rate in acres per hour from a nonnegative area and a positive elapsed time. Animal Mortality Rate Calculate an interval mortality rate per 1,000 and as a percentage from deaths and the number surviving at the interval start. Annealing Temperature Quick Screen Estimate a short oligo melting temperature with the educational Wallace count rule, subtract an offset for a screening annealing temperature, and report GC percentage. Bacteria Growth Calculate continuous idealized population growth from an initial population, a positive doubling time, and elapsed hours. Basal Area From Diameter Estimate circular cross-sectional area per stem and in total from a supplied diameter and a safe stem count. Bulb Spacing Area Estimate Estimate the number of equally spaced bulbs for a rectangular bed using a square-grid footprint and a whole-unit ceiling. Cattle Per Acre Calculate a descriptive cattle-per-acre rate from a safe whole-number cattle count and positive acreage. Cell Doubling Time From Observations Estimate an idealized doubling time from positive observed populations, a larger final observation, and elapsed hours. Corn Harvest Density Calculate descriptive harvested corn mass per hectare from an entered mass and harvested area. Dihybrid Cross Punnett Square Calculate genotype and simplified phenotype percentages for a two-locus cross using nine canonical parent genotypes. DNA Concentration Calculate DNA mass concentration from an entered mass and sample volume, with equivalent ng/uL and ug/mL outputs. DNA Copy Number From Mass Estimate the number of double-stranded DNA molecules from mass and a safe whole-number base-pair length. Shannon Diversity Index Calculate descriptive Shannon diversity and evenness from a bounded list of entered species or group counts. Hydroelectric Power Calculate idealized hydraulic and delivered electrical power from entered water flow, hydraulic head, and efficiency. Solar Panel Wattage Calculate idealized instantaneous solar-panel power from entered irradiance, panel area, and conversion efficiency. Wind Turbine Power Calculate idealized kinetic wind power and estimated turbine power from entered air density, swept area, wind speed, and power coefficient. Torque from Force and Lever Arm Calculate the magnitude of torque from a force, lever-arm length, and the angle between them. Angular Momentum of a Point Mass Calculate angular momentum magnitude for a point mass moving tangentially at a stated radius and speed. Rotational Kinetic Energy Calculate the rotational kinetic energy of an ideal rigid body from its moment of inertia and angular speed. Elastic Potential Energy Calculate the elastic potential energy stored in an ideal linear spring from its spring constant and displacement. Gravitational Force Between Two Point Masses Calculate the magnitude of Newtonian gravitational force between two point masses at a stated separation. Escape Velocity Calculate the classical escape velocity at the surface of an ideal spherical body from its mass and radius. Latent Heat Calculate the energy required for a phase change from mass and specific latent heat. Linear Thermal Expansion Calculate length change and final length from initial length, linear expansion coefficient, and temperature change. Coulomb's Law Calculate the magnitude and attraction or repulsion relationship for two point charges at a stated separation. Magnetic Force on a Current-Carrying Wire Calculate the magnetic-force magnitude on a straight current-carrying wire in a uniform magnetic field. Snell's Law Calculate the refracted angle from two refractive indices and an incident angle, including a total-internal-reflection result when appropriate. Thin Lens Equation Calculate image distance and magnification from a signed focal length and positive object distance. Diffraction-Limited Angular Resolution Calculate the Rayleigh diffraction-limit angular resolution of a circular aperture from wavelength and diameter. Stefan-Boltzmann Law Calculate ideal thermal-radiation power from emissivity, radiating area, and absolute temperature. Wien's Displacement Law Calculate the ideal blackbody peak wavelength from absolute temperature. Angular Acceleration Calculate average angular acceleration from initial angular velocity, final angular velocity, and a positive time interval. G-Force from Acceleration Express a supplied acceleration magnitude as a multiple of standard gravity without calculating force in newtons. Stellar Parallax Distance Calculate an astronomical distance from a positive stellar parallax entered in arcseconds, reporting parsecs and light-years. Circular Two-Body Orbital Velocity Calculate the Newtonian relative speed for two positive masses in a circular orbit at a stated center-to-center separation. Special-Relativistic Time Dilation Calculate proper elapsed time from a coordinate-time interval and a subluminal speed using the special-relativistic inertial-clock relation. Empirical Formula Determine an empirical formula from mass percentages for two to twelve supported elements. Molality Calculate solution molality from solute amount and the mass of solvent in kilograms. Freezing-Point Depression Estimate the freezing-point decrease and solution temperature for a dilute ideal solution. Raoult's Law Calculate a volatile solvent mole fraction, ideal solution vapor pressure, and pressure lowering. PPM to Molarity Convert a mass-based ppm concentration into molarity and mass concentration using solution density. Mass-Energy Equivalence (E=mc^2) Calculate the rest energy represented by a mass using the special-relativity equivalence E0 = mc^2. Relativistic Kinetic Energy Calculate kinetic energy from mass and speed as a fraction of the speed of light using the Lorentz factor. Relativistic Velocity Addition Combine two signed collinear subluminal velocities using the special-relativistic velocity-addition formula. Hooke's Law Spring Force Calculate the ideal restoring force and its magnitude from a linear spring constant and signed displacement. Carnot Efficiency Limit Calculate the ideal reversible Carnot efficiency limit from hot- and cold-reservoir temperatures in kelvins. Index of Refraction from Light Speed Calculate a medium's refractive index and light-speed fraction from its supplied light speed. Beat Frequency Calculate the ideal beat frequency produced by two entered frequencies. Doppler Effect Moving Source Calculate the observed frequency and shift for a stationary observer and a one-dimensional moving source in a still medium. Heisenberg Position-Momentum Uncertainty Calculate the minimum momentum uncertainty associated with a positive position uncertainty using the one-dimensional Heisenberg bound. Two-Body Thermal Equilibrium Temperature Calculate the final equilibrium temperature and signed heat transfer for two bodies sharing heat in an isolated constant-specific-heat model. Cyclotron Frequency, Angular Frequency, and Period Calculate the angular frequency, ordinary frequency, and period of a signed charged particle in a positive magnetic field. Malus's Law Polarized Intensity Calculate transmitted intensity and the ideal transmission fraction for linearly polarized light passing through an analyzer at a stated angle. Kepler's Third Law Two-Body Orbital Period Calculate a Newtonian two-body orbital period in seconds and days from semimajor axis and primary and secondary masses. Voltage Drop Calculator Calculate two-conductor voltage drop from current, one-way length, resistance, and source voltage. Wind Chill Calculator Calculate the National Weather Service wind-chill index for Fahrenheit air temperatures and wind speeds. Heat Index Calculator Calculate the National Weather Service Rothfusz heat-index estimate from Fahrenheit temperature and humidity. Dew Point Calculator Estimate dew point from Celsius air temperature and relative humidity with the Magnus approximation. Torque and Horsepower Calculator Convert torque and rotational speed into watts, kilowatts, and mechanical horsepower.

Total-Period Return on Investment Measure an investment's total-period gain or loss relative to its full cost, with proceeds explicitly including recovered principal and no unsupported payback-year estimate. Whole-Unit Break-Even Point Calculate the whole units needed to cover fixed costs and the matching revenue, alongside the theoretical fractional-unit threshold and contribution per unit. Target Margin or Markup Pricing Set a selling price using either a profit-margin target or a markup-on-cost target, and see both percentages so their different denominators are never confused. Net Cash Burn and Runway Estimate how long available cash lasts after accounting for monthly cash receipts and expenses, and distinguish positive burn from cash flows that do not deplete the balance. Entered-Rate Tax Addition or Removal Add a user-entered percentage tax to a base amount or recover the pre-tax amount from an inclusive total, without assuming a location, current rate, or legal tax treatment. Single or Sequential Discounts Calculate the sale price, total savings, and effective percentage reduction for one discount or two discounts applied sequentially rather than added together. Profit Margin and Markup Analysis Measure profit or loss from matched revenue and costs, showing margin on revenue separately from markup on cost, including loss-making and zero-cost cases. Straight-Line Depreciation Spread an asset's depreciable cost evenly over its useful life. Economic Order Quantity (EOQ) Optimal order size balancing ordering and holding costs. Target-Profit Sales Units Units to sell to cover fixed costs plus a profit target. Liquidity Ratios (Current and Quick) Short-term financial health from current assets and liabilities. Double-Declining Depreciation Accelerated depreciation schedule floored at salvage value. Price Elasticity of Demand (Midpoint) Demand responsiveness free of start-point bias, with elastic/inelastic verdict. Freelance Hourly Rate from Salary Billable rate covering salary, costs, and non-billable time. Margin of Safety How far sales can fall before losses, in currency and percent. Inventory Turnover and Days How fast stock sells through, plus days of inventory on hand. Inventory Reorder Point Stock level triggering a new order from daily use and lead time. Sales Commission Paycheck Take-home from base salary plus commission on sales. GDP by Expenditure Gross domestic product from consumption, investment, government, and net exports. Unemployment Rate Share of the labor force without work from two headcounts. Money Multiplier Maximum deposit expansion from a reserve ratio. Break-Even Units Calculator Find the unit sales and revenue needed to cover fixed costs when price and variable cost are known. Average Fixed Cost Calculator Calculate fixed cost per unit from total fixed costs and output quantity. Defects per Million Opportunities Calculator Calculate defects per million opportunities from defects, units, and opportunities per unit. Billable Hours and Revenue Calculator Estimate billable hours and gross revenue from available work hours, a billable utilization rate, and an hourly rate. Required Billable Rate Calculator Calculate the hourly billable rate needed to cover a target income and overhead across planned billable hours. 3D Printer Buy-or-Outsource Calculator Compare a fixed printer purchase plus in-house unit cost with a per-unit outsourcing price and find a simple break-even quantity. Absence Percentage Calculator Calculate absent days, attended days, and absence percentage from scheduled and missed days. Average Daily Room Rate Calculator Calculate hospitality average daily rate and occupancy from room revenue, rooms sold, and available room-nights. Employee Attrition Rate Calculator Calculate attrition and retention percentages from departures and average headcount over a selected period. Website Bounce Rate Calculator Calculate bounce and engaged-session percentages from single-page sessions and total sessions. PERT Three-Point Schedule Estimate Combine optimistic, most-likely, and pessimistic task durations into a weighted expected time, spread, and variance for early project planning. Takt Time Calculate the production pace required to meet demand from effective available time and demand per period. CV Screening and Interview Time Calculator Estimate recruiting workload from applicant count, review time, shortlist rate, interview rounds, and available workday hours. Marginal Cost Calculator Calculate the average marginal cost over an output interval from two total-cost observations and two production quantities. Marginal Revenue Calculator Calculate the average marginal revenue over a quantity interval from two total-revenue observations. Hire an Expert vs Train a Fresher Calculator Compare entered hiring, compensation, training, ramp-up, and planning-horizon assumptions for an experienced hire versus a new starter. Production Cycle Time Calculator Estimate total elapsed production time, average minutes per unit, and hourly throughput from batch, run-time, changeover, transfer, and parallel-station assumptions. Customer Acquisition Cost (CAC) Average fully-loaded spend required to win one new customer. Sales Funnel Conversion Rates Signup, visitor-to-buyer, and signup-to-buyer rates from three funnel stages. Overtime Pay Weekly paycheck split into regular and overtime pay at an adjustable threshold and multiplier. Contribution Margin Contribution margin dollars and ratio from sales and variable costs. Receivables Turnover and DSO Collection turns per year and days sales outstanding from credit sales. Debt-to-Equity Ratio Creditor versus owner financing per unit of equity. DuPont ROE Return on equity from margin, asset turnover, and leverage. Cost of Goods Sold Build COGS from beginning inventory, purchases, and ending inventory. Consumer Surplus Triangle Consumer surplus as the triangle under linear demand. Per-Capita Value Average per-person share of any aggregate total. Simple Customer Lifetime Value Lifetime margin from yearly margin times relationship length. Market Share Firm's percentage of total market sales. Two-Stage Markup Chain Wholesale then retail price from cost plus two margins on selling price. Project Buffer Contingency hours and padded total from a base estimate. Volumetric Shipping Weight Billable dimensional weight from package size and carrier divisor. Predetermined Overhead Rate Overhead rate from estimated cost and base. Sales Quota Tracker Attainment percent and remaining amount to quota. Direct Cost Variances Splits a cost gap into price and efficiency variances with U/F verdicts. Total Revenue Test Compares total revenue before and after a price change. Real Value from GDP Deflator Deflates a nominal amount into base-year dollars. CPI Inflation Rate Computes inflation between two CPI readings. A/B Two-Proportion Z-Test Tests whether two conversion rates differ at 5% significance. Checkout Total with Tip Adds discount, tax, and tip in the right order for a final bill. Customer Lifetime Value with Retention Estimates undiscounted customer lifetime value from order value, purchase frequency, gross margin, and annual churn. Price Ceiling Shortage Sketch Checks whether an entered price ceiling binds and reports the quantity gap at the supplied demand and supply values. Accounting Equation Check Check whether entered assets, liabilities, and equity satisfy the fundamental accounting equation. Working Capital Calculator Calculate working capital as current assets minus current liabilities for one reporting date. Cash Reconciliation Calculator Reconcile beginning cash with operating, investing, and financing cash flows to estimate ending cash. Retained Earnings Calculator Calculate ending retained earnings from beginning retained earnings, net income, and dividends. Cash Ratio Calculator Calculate the cash ratio from cash, cash equivalents, and current liabilities. Equity Multiplier Calculator Calculate the equity multiplier by dividing total assets by total equity. Cash Conversion Cycle Calculator Calculate the cash conversion cycle from inventory, receivables, and payables day assumptions. Degree of Operating Leverage Calculator Calculate the static-period degree of operating leverage from contribution margin and operating income. Times Interest Earned Calculator Calculate times interest earned by dividing EBIT by interest expense for one period.

Running Pace and Speed Calculator Calculate average running pace and speed from distance and elapsed time. Bowling Average Calculator Calculate a simple bowling average from total runs and completed innings or games. Cycling Cadence Calculator Estimate wheel speed and crank cadence from road speed, wheel diameter, and a wheel-to-crank ratio. Batting Strike Rate Calculator Calculate a cricket batting strike rate from runs scored and legal balls faced. Bicycle Gear Ratio Calculator Calculate bicycle gear ratio and mechanical distance per crank revolution from front and rear sprocket teeth. Elo Rating Update Calculator Calculate expected score and a new Elo rating from two ratings, a K-factor, and an entered match result. Cycling Power Estimate Estimate steady cycling power from mass, speed, road grade, rolling resistance, and aerodynamic drag inputs. Ape Index Calculator Calculate the difference and ratio between arm span and height as a simple body-proportion measure. Vertical Jump Requirement Calculator Calculate the vertical jump required to clear a target height from standing reach and a desired clearance margin. Bicycle Frame Size Estimate Estimate a bicycle frame size from inseam length and a selected road or mountain-bike multiplier. E-Bike Range Estimate Estimate electric-bike travel range from battery energy, usable efficiency, reserve, and energy consumption per distance. Fishing Reel Line Capacity Calculator Estimate line length on a cylindrical spool from outer diameter, core diameter, spool width, and line diameter. Bicycle Speed from Cadence Calculator Calculate bicycle speed from wheel diameter, cadence, and a wheel-to-crank distance ratio. Hiking Time with Elevation Calculator Estimate hiking time from horizontal distance, base speed, elevation gain, and a supplied climbing speed. Displacement Hull Speed Calculator Estimate a traditional displacement-hull speed from waterline length using a supplied hull-speed coefficient. Walking Stride Length Calculator Calculate average stride length from walking distance and step count, with a metres-per-step result. Steps to Distance Calculator Estimate walking distance from step count and an explicitly supplied average stride length. Pool Table Room Size Calculator Calculate minimum room length, width, and area from table dimensions and cue clearance on every side. 0–60 Acceleration Calculator Estimate average acceleration and travel distance for a 0-to-speed run from elapsed time under a constant-acceleration model. Bench Press One-Rep-Max Estimate Estimate a bench-press one-repetition maximum from a lifted load and completed repetitions using the Epley relation. Bicycle Chain Length Estimate Estimate bicycle chain length in chain pitches from center distance and front and rear sprocket tooth counts. Fish Weight Estimate from Length and Girth Estimate fish mass from entered length, girth, and a visible species or unit coefficient. Generic Game Score Calculator Add scored events with entered point values to calculate a transparent team or game score. Pace and Speed Calculator Calculate average pace and speed from a distance, elapsed time, and the distance unit you use. 5K Pace Calculator Convert a 5-kilometre finish time into average kilometre and mile pace and speed. Half-Marathon Pace Calculator Calculate average pace and speed for a half-marathon from a finish time. Marathon Pace Calculator Calculate average marathon pace and speed from a full-marathon finish time. Cycling Pace and Moving Speed Calculator Separate moving time from stop time to estimate cycling pace, moving speed, and elapsed speed. Bike Cadence and Speed Calculator Estimate bicycle speed from wheel diameter, pedalling cadence, and wheel-to-crank gear ratio. Race Time Predictor Project a target race time from a completed distance and time using an adjustable endurance exponent. Training Pace Calculator Estimate a target training pace from a reference performance, target distance, and selected effort percentage. Walking Calorie Estimate Estimate walking energy from body mass, duration, speed, and uphill or downhill grade using a transparent exercise equation. Running Calorie Estimate Estimate running energy from body mass, distance, and a user-selected terrain factor. Jump-Rope Calorie Estimate Estimate jump-rope energy from body mass, duration, and a selected rope-skipping intensity. Stair-Climbing Energy Calculator Estimate the energy needed to raise a body through a number of stair flights using gravitational work and an efficiency assumption. Steps to Calories Estimate Convert steps into an estimated walking distance and energy using stride length and an explicit energy-per-distance assumption. Steps to Miles and Kilometres Calculator Estimate walking distance from a step count and average stride length in both kilometres and miles. Hiking Time Estimate Estimate hiking time from horizontal distance, elevation gain, terrain factor, and planned rest time. Triathlon Time Calculator Add swim, bike, run, and transition estimates to plan a total triathlon time. Swimming Time Calculator Estimate total swim-session time from distance, pace per 100 metres, and planned rest intervals. Cycling Power Zones Calculator Build cycling power zones from functional threshold power using a selectable five-zone or seven-zone percentage scheme. Target Heart-Rate Range Calculator Estimate a heart-rate range with the heart-rate-reserve method from age, resting pulse, and two intensity percentages. Heart-Rate Recovery Calculator Calculate the one-minute heart-rate drop and normalized recovery from resting, peak, and post-exercise heart rates. Poker Drawing Odds from Outs Calculate the chance of hitting at least one out by the next one or two cards from unseen-card count. Poker Expected Value of a Call Estimate the expected profit or loss of a poker call from win, tie, pot, and call-cost assumptions. Fielding Independent Pitching Calculate a baseball pitcher's FIP-style estimate from home runs, walks, hit batters, strikeouts, innings, and a chosen league constant. NFL-Style Passer Rating Calculator Calculate the NFL-style passer rating from attempts, completions, passing yards, touchdowns, and interceptions. Cricket Net Run Rate Calculator Calculate a cricket team's net run rate from runs scored, runs conceded, and the legal balls in each innings sample. MET-Minutes per Week Calculator Estimate weekly MET-minutes from activity intensity, session duration, and sessions per week, with time-equivalent views. Cooper 1.5-Mile VO₂ Max Estimate Estimate VO₂ max from a timed 1.5-mile run or walk using the Cooper Institute field-test equation. Race Split Planner Build an even split schedule from a target distance, finish time, and split length, including the final partial split when the distances do not divide evenly. Rowing Erg Pace and Watts Calculator Calculate rowing-erg work time, 500-metre split pace, average speed, estimated watts, and total session time for repeated intervals with optional rest. Cycling Breakaway Gap Planner Estimate how a speed difference changes a cycling breakaway's physical gap over a selected time horizon and when a target gap could be reached. Bench Press Pyramid Volume Planner Build a transparent ascending or descending bench-press percentage pyramid from a user-entered one-rep maximum, set count, repetitions, and percentage step. Ski Length Range Scenario Calculator Create a transparent ski-length range from height, ability, terrain, and editable shorter- and longer-end adjustments instead of presenting one universal ski size. Tennis Ball Inventory Planner Estimate match balls, practice balls, replacement allowance, and cans needed for a tennis event or training block using editable event rules. Cricket Follow-On Lead Calculator Check a first-innings lead against the selected match duration and show the shortfall or margin for a follow-on option. Bruce Protocol METs Estimate Estimate treadmill workload, oxygen uptake, and METs for a selected stage of the standard Bruce exercise-testing protocol. Women’s Heptathlon Points Calculator Estimate points for the seven events in a women’s heptathlon and show track, field, event, and total scores. Wilks Powerlifting Score Calculator Calculate the historical Wilks coefficient and bodyweight-adjusted powerlifting score from category, body weight, and total. 5/3/1 Training-Max Percentage Calculator Plan three working sets from a 5/3/1 training max, selected week, and equipment rounding increment. Baseball Magic Number Calculator Calculate the standings combination of wins and opponent losses needed to clinch a baseball goal from the loss-column gap and games remaining. Human Punch Force Estimate Estimate average model force, impulse, velocity change, and kinetic energy from effective striking mass, acceleration, and contact time. Age-Graded Running Calculator Compare a runner's entered race time with an age-and-category reference standard, then show age grade, time gap, pace, and speed without pretending to supply an official table. Anaerobic Threshold Field-Test Calculator Estimate a threshold heart rate and pace from a controlled time trial, show heart-rate drift, and display transparent planning screens with clear limits. Triathlon Finish-Time Breakdown Calculator Add swim, bike, run, and transition times for a sprint, standard, or custom course and show total time, discipline shares, pace, and speed. Magic Mile Race-Time Predictor Project a target running time from a measured mile using a transparent distance-power model, with target pace, speed, and model cost shown together. Triathlon Training-Load Planner Project weekly training hours through a build and taper using explicit progression, reduction, and session-count inputs, with a transparent workload summary. Cricket Rain-Interrupted Target Calculator Apply supplied first- and second-innings resource percentages to estimate a revised cricket target, while keeping the resource-ratio method separate from official professional tables. ICC T20 Team Ranking Points Calculator Project one team's match points and updated rating from two supplied team ratings, a result, and the number of matches already represented in the average. Windsurfing Apparent-Wind and Sail-Force Calculator Resolve true wind and board motion into apparent wind, dynamic pressure, and a transparent sail-force screen for a simplified windsurfing physics scenario. Heart-Rate Energy Estimate Calculator Estimate exercise energy from average heart rate, body mass, age, equation branch, and duration using a transparent population-derived heart-rate model. Snow-Shoveling Energy Calculator Estimate total and active-above-rest energy for manual snow shoveling from body mass, duration, and moderate or vigorous activity intensity. Race Time Improvement Calculator Apply a chosen percentage improvement to a current race time and show the faster target, seconds saved, and equivalent minutes saved. Goalkeeper Save Percentage Calculator Calculate save percentage, shots not saved, concession percentage, and shots faced per save from a defined shot sample. Fat-Burning Heart-Rate Zone Calculator Compare percentage, Karvonen heart-rate-reserve, and Zoladz reference ranges from age, resting heart rate, and a maximum-heart-rate choice. Scuba Neutral-Buoyancy Ballast Estimate Estimate the ballast mass needed for a simplified neutral-buoyancy scenario from diver, equipment, suit, cylinder, gas, and water-density inputs. Kiteboarding Apparent Wind and Force Screen Estimate apparent wind, aerodynamic dynamic pressure, lift, drag, and resultant kite force from wind, rider speed, angle, kite area, and coefficients. Batting Average Calculate a baseball hitter's batting average from hits and at-bats. On-Base Percentage Calculate baseball on-base percentage from hits, walks, hit-by-pitches, at-bats, and sacrifice flies. Slugging Percentage Calculate baseball slugging percentage from hit-type counts and at-bats. On-Base Plus Slugging Add already-calculated on-base and slugging percentages to obtain OPS. Earned Run Average Calculate a baseball pitcher's earned-run average from earned runs and recorded outs. Baseball WHIP Calculate walks plus hits per inning pitched from a baseball pitching line. Fielding Percentage Calculate a baseball fielder's fielding percentage from putouts, assists, and errors. Effective Field Goal Percentage Calculate basketball effective field goal percentage while giving made three-pointers extra shot value. True Shooting Percentage Estimate basketball true shooting percentage from points, field-goal attempts, and free-throw attempts. Faceoff Win Percentage Calculate a hockey player's faceoff win percentage from wins and losses. Goalie Save Percentage Calculate a hockey goaltender's save percentage from saves and goals allowed. Goals-Against Average Calculate a hockey goaltender's goals-against average from goals allowed and minutes played. Winning Percentage Calculate a team's or player's win rate from wins and losses.