Statistics Calculators

Average, Median, and Summary Calculator

Summarize a numeric list with its arithmetic mean, median, sum, count, minimum, and maximum.

You enter: Values

Example: 5

Open Average, Median, and Summary Calculator →

Standard Deviation and Variance Calculator

Measure data spread using population or sample standard deviation, with variance and mean.

You enter: Values · Data interpretation

Example: 2

Open Standard Deviation and Variance Calculator →

Z-Score Calculator

Express an observation's distance from a mean in standard-deviation units.

You enter: Observed value · Mean · Standard deviation

Example: 1.5

Open Z-Score Calculator →

Five-Number Summary and Outliers

Minimum, quartiles, median, maximum, IQR, and outlier fences for a data list.

You enter: Values

Example: Min 2; Q1 4; median 4.5; Q3 6; max 9; IQR 2; no outliers.

Open Five-Number Summary and Outliers →

Expected Value (Discrete)

Mean outcome of a gamble or lottery from values and probabilities.

You enter: Outcome values · Matching probabilities

Example: Expected value: 20.

Open Expected Value (Discrete) →

Summary Statistics Calculator

Find the count, mean, median, mode, and range of a numeric list.

You enter: Numbers

Example: Count = 5; mean = 8; median = 7; mode = 7; range = 9.

Open Summary Statistics Calculator →

Variance and Standard Deviation Calculator

Calculate population and sample variance and standard deviation from a numeric list.

You enter: Numbers

Example: Mean = 5; population variance = 4; sample variance ≈ 4.571; sample SD ≈ 2.138.

Open Variance and Standard Deviation Calculator →

Weighted Average Calculator

Calculate a weighted average from comma-separated values and matching nonnegative weights.

You enter: Values · Weights

Example: Weighted average = 20.

Open Weighted Average Calculator →

Cohen's d Effect Size Calculator

Calculate the standardized mean difference between two independent groups using pooled sample standard deviation.

You enter: Group 1 mean · Group 1 sample SD · Group 1 sample size · Group 2 mean · Group 2 sample SD · Group 2 sample size

Example: Pooled SD ≈ 9.142; Cohen's d ≈ 0.547.

Open Cohen's d Effect Size Calculator →

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.

You enter: Between-group sum of squares · Within-group sum of squares · Between-group degrees of freedom · Within-group degrees of freedom

Example: MS between=40; MS within=8.333; F=4.8.

Open One-Way ANOVA F Statistic Calculator →

Five-Number Box Plot Summary Calculator

Calculate minimum, first quartile, median, third quartile, and maximum from a numeric list using Tukey hinges.

You enter: Data values

Example: Five-number summary =1, 2.5, 5, 7.5, 9.

Open Five-Number Box Plot Summary Calculator →

Chebyshev Theorem Coverage Calculator

Calculate the guaranteed minimum fraction within k standard deviations of a mean.

You enter: Number of standard deviations k

Example: At least 75% lies within 2 standard deviations.

Open Chebyshev Theorem Coverage Calculator →

Descriptive Statistics Summary Calculator

Calculate population-style mean, median, range, variance, and standard deviation for a finite numeric list.

You enter: Data values

Example: Mean =8; median =7; range =9; population standard deviation ≈3.033.

Open Descriptive Statistics Summary Calculator →

Independent Groups Standardized Difference Calculator

Calculate the standardized mean difference between two independent groups using a pooled standard deviation.

You enter: Group A mean · Group B mean · Group A standard deviation · Group B standard deviation · Group A sample size · Group B sample size

Example: Pooled SD ≈11.0; Cohen's d ≈0.545.

Open Independent Groups Standardized Difference Calculator →

Mean Median and Mode Calculator

Calculate mean, median, and repeated-value mode information for a finite numeric list.

You enter: Data values

Example: Mean =4.2; median =3; mode =3.

Open Mean Median and Mode Calculator →

Mean Squared Error and RMSE Calculator

Calculate mean squared error and root mean squared error from equal-length actual and predicted lists.

You enter: Actual values · Predicted values

Example: MSE =1; RMSE =1.

Open Mean Squared Error and RMSE Calculator →

Exponential Model Prediction Calculator

Evaluate an exponential prediction model from a starting value, continuous rate, and elapsed time.

You enter: Initial value · Continuous rate · Elapsed time

Example: Predicted value ≈164.872.

Open Exponential Model Prediction Calculator →

Five-Star Rating Summary Calculator

Calculate review count, average star rating, and share of four-or-five-star ratings from star counts.

You enter: 1-star count · 2-star count · 3-star count · 4-star count · 5-star count

Example: Total reviews =100; average =4.53; favorable share =90%.

Open Five-Star Rating Summary Calculator →

Relative Standard Deviation Calculator

Calculate relative standard deviation as a ratio and percentage from standard deviation and mean.

You enter: Standard deviation · Mean

Example: RSD =0.08; percentage RSD =8%.

Open Relative Standard Deviation Calculator →

Trimmed Mean Calculator

Calculate a two-sided trimmed mean by removing the same percentage of low and high observations.

You enter: Data values · Trim from each tail

Example: Trim 1 from each tail; trimmed mean =35.

Open Trimmed Mean Calculator →

Mean Absolute Deviation Calculator

Calculate the arithmetic mean and the average absolute distance from that mean.

You enter: Data values

Example: Mean =4.6; mean absolute deviation =2.72.

Open Mean Absolute Deviation Calculator →

Coefficient of Variation Calculator

Calculate relative spread by dividing population standard deviation by the absolute arithmetic mean.

You enter: Data values

Example: Mean =100; CV ≈9.49%.

Open Coefficient of Variation Calculator →

Standard Error of the Mean Calculator

Calculate the standard error and variance of a sample mean from a standard deviation and sample size.

You enter: Standard deviation · Sample size n

Example: Standard error =2.5; variance of mean =6.25.

Open Standard Error of the Mean Calculator →

Pooled Variance Calculator

Calculate pooled variance and pooled standard deviation for two independent groups.

You enter: Group 1 standard deviation · Group 1 sample size · Group 2 standard deviation · Group 2 sample size

Example: Pooled variance ≈121.214; pooled SD ≈11.010.

Open Pooled Variance Calculator →

Welch Degrees of Freedom Calculator

Calculate the Welch–Satterthwaite degrees of freedom for an unequal-variance two-sample mean comparison.

You enter: Group 1 standard deviation · Group 1 sample size · Group 2 standard deviation · Group 2 sample size

Example: Welch degrees of freedom ≈52.72.

Open Welch Degrees of Freedom Calculator →

Discrete Expected Value Calculator

Calculate the expected value and variance of a discrete distribution from paired outcomes and probabilities.

You enter: Outcomes · Probabilities

Example: Expected value =1.1; variance =0.49.

Open Discrete Expected Value Calculator →

Binomial Mean and Variance Calculator

Calculate the expected successes, variance, and standard deviation for a binomial model.

You enter: Number of trials n · Success probability p

Example: Expected successes =8; variance =4.8; standard deviation ≈2.191.

Open Binomial Mean and Variance Calculator →

Geometric Waiting-Time Mean Calculator

Calculate the mean and variance of the number of trials until the first success in a geometric model.

You enter: Success probability p

Example: Expected trials =4; variance =12.

Open Geometric Waiting-Time Mean Calculator →

Pearson Median Skewness Calculator

Calculate Pearson’s second skewness coefficient from the mean, median, and standard deviation.

You enter: Mean · Median · Standard deviation

Example: Pearson skewness =1.

Open Pearson Median Skewness Calculator →

Glass’s Delta Effect Size Calculator

Calculate Glass’s delta using the control-group standard deviation as the reference scale.

You enter: Treatment mean · Control mean · Control standard deviation

Example: Glass’s delta =0.7.

Open Glass’s Delta Effect Size Calculator →

F-Statistic Calculator

Calculate the ratio of two entered variances for a simple F-statistic scenario.

You enter: Numerator variance · Denominator variance

Example: F-statistic = 1.5625.

Open F-Statistic Calculator →

One-Sample t-Statistic Calculator

Calculate a one-sample t statistic, standard error, and degrees of freedom from summary statistics.

You enter: Sample mean · Hypothesized mean · Sample standard deviation · Sample size

Example: Standard error = 2; t = 2.5; degrees of freedom = 24.

Open One-Sample t-Statistic Calculator →

Grouped Data Standard Deviation Calculator

Estimate weighted mean and population or sample standard deviation from class midpoints and frequencies.

You enter: Class midpoints · Class frequencies

Example: Weighted mean ≈ 26.47; population standard deviation ≈ 9.037.

Open Grouped Data Standard Deviation Calculator →

Relative Standard Error Calculator

Calculate the standard error and relative standard error of a sample mean from a data list.

You enter: Sample values

Example: Mean = 10; standard error ≈ 0.7071; relative standard error ≈ 7.071%.

Open Relative Standard Error Calculator →

Sum of Squares Calculator

Calculate the squared-deviation total, mean squared deviation, and root-mean-square distance from a reference value.

You enter: Values · Reference value

Example: Sum of squares = 30; mean squared distance = 7.5; RMS distance ≈ 2.739.

Open Sum of Squares Calculator →

Upper Control Limit Calculator

Calculate center, upper, and lower three-sigma-style limits for a sample-mean control chart.

You enter: Process mean · Process standard deviation · Subgroup size · Sigma multiplier

Example: Center = 100; UCL ≈ 105.367; LCL ≈ 94.633.

Open Upper Control Limit Calculator →

Raw Score Calculator

Convert a z-score into a raw score using a supplied mean and standard deviation.

You enter: Mean · Standard deviation · z-score

Example: Deviation = 30; raw score = 130.

Open Raw Score Calculator →

Five-Number Summary Calculator

Sort five observations and report the minimum, first quartile, median, third quartile, and maximum.

You enter: Observation 1 · Observation 2 · Observation 3 · Observation 4 · Observation 5

Example: Summary: minimum 2, Q1 4, median 6, Q3 7, maximum 9.

Open Five-Number Summary Calculator →

Mean Absolute Deviation for Five Values

Calculate the mean, mean absolute deviation, and largest absolute deviation for five observations.

You enter: Observation 1 · Observation 2 · Observation 3 · Observation 4 · Observation 5

Example: Mean: 9; mean absolute deviation: 2.8; largest absolute deviation: 6.

Open Mean Absolute Deviation for Five Values →

Median Calculator for Five Values

Sort five numeric values and calculate their median, mean, and distance between the extreme values.

You enter: Value 1 · Value 2 · Value 3 · Value 4 · Value 5

Example: Median: 9; mean: 11.4; range: 21.

Open Median Calculator for Five Values →

Mode Calculator for Five Values

Find the unique most frequent value in a five-observation dataset and report its frequency and share.

You enter: Value 1 · Value 2 · Value 3 · Value 4 · Value 5

Example: Mode: 3; frequency: 2 of 5; modal share: 40%.

Open Mode Calculator for Five Values →

Pooled Standard Deviation Calculator

Combine two sample standard deviations using their degrees of freedom to estimate a common pooled spread.

You enter: Group 1 sample standard deviation · Group 1 sample size · Group 2 sample standard deviation · Group 2 sample size

Example: Pooled standard deviation: about 10.65; pooled degrees of freedom: 48.

Open Pooled Standard Deviation Calculator →

Population Variance Calculator

Calculate the population mean, population variance, standard deviation, and root-mean-square value for five values.

You enter: Value 1 · Value 2 · Value 3 · Value 4 · Value 5

Example: Mean: 6; population variance: 8; standard deviation: 2.828.

Open Population Variance Calculator →

Quartile Calculator for Nine Values

Sort nine observations and calculate Q1, median, Q3, interquartile range, and the quartile midhinge.

You enter: Value 1 · Value 2 · Value 3 · Value 4 · Value 5 · Value 6 · Value 7 · Value 8 · Value 9

Example: Q1: 6; median: 10; Q3: 15; IQR: 9.

Open Quartile Calculator for Nine Values →

Sampling Standard Error Calculator

Calculate the standard error of a sample mean and an illustrative 95% normal-approximation margin.

You enter: Sample standard deviation · Sample size n

Example: Standard error: 2; illustrative 95% margin: 3.92.

Open Sampling Standard Error Calculator →

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.

You enter: Citations in the current year to the selected two-year window · Scholarly items published in the selected two-year window

Example: Impact-factor style rate = 2.5 citations per item.

Open Journal Impact Factor Arithmetic Calculator →

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.

You enter: Data values

Example: Ordered values are 4, 7, 10, 12, 15, 19, 21; Q3 is 19, Q1 is 7, and IQR is 12.

Open Third Quartile Calculator →

Sample or Population Variance Calculator

Calculate variance and standard deviation from a pasted dataset while keeping the population or sample divisor explicit.

You enter: Data values · Variance convention

Example: The sample mean is 9; sample variance is 16.5 and sample standard deviation is about 4.0620.

Open Sample or Population Variance Calculator →

Standard Deviation and Standard Error from Data

Calculate a sample standard deviation, standard error of the mean, and relative standard error from raw observations.

You enter: Sample values

Example: Sample standard deviation is about 4.0620; standard error is about 1.8166; relative standard error is about 20.184%.

Open Standard Deviation and Standard Error from Data →

Frequency Polygon Point Calculator

Convert class midpoints and frequencies into frequency-polygon points, total frequency, and a grouped weighted mean.

You enter: Class midpoints · Class frequencies

Example: Total frequency is 17; grouped mean is about 4.2941; points are (1,2), (3,5), (5,7), (7,3).

Open Frequency Polygon Point Calculator →

Expected Dice Average Calculator

Calculate the expected value, variance, standard deviation, and possible range for a sum of fair identical dice.

You enter: Sides per die · Number of dice

Example: Two fair six-sided dice have expected sum 7, variance 35/6 ≈ 5.8333, standard deviation ≈ 2.4152, and range 2–12.

Open Expected Dice Average Calculator →

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.

You enter: Chord-selection model · Circle radius

Example: The threshold is √3 ≈ 1.732 units and the two-random-endpoints model gives probability 1/3 ≈ 33.33%.

Open Bertrand Chord Probability Model Calculator →

Empirical Rule Bands

68-95-99.7% intervals from mean and standard deviation.

You enter: Mean · Standard deviation

Example: 68% (85, 115); 95% (70, 130); 99.7% (55, 145).

Open Empirical Rule Bands →

Root Mean Square

Calculate the root mean square of a bounded list of numeric values.

You enter: Values

Example: Root mean square 3.535534.

Open Root Mean Square →

Geometric Mean

Calculate the geometric mean of a list of positive values using logarithmic accumulation for stability.

You enter: Positive values

Example: Geometric mean 4.

Open Geometric Mean →

Harmonic Mean

Calculate the harmonic mean of a list of positive values.

You enter: Positive values

Example: Harmonic mean 3.2.

Open Harmonic Mean →

Coefficient of Variation

Calculate the sample standard deviation relative to a positive sample mean.

You enter: Sample values

Example: Mean 10, sample standard deviation 2, coefficient of variation 20%.

Open Coefficient of Variation →

Sample Covariance

Calculate the sample covariance of two equal-length paired data sets.

You enter: X values · Y values

Example: Sample covariance is 2.5.

Open Sample Covariance →

Median Absolute Deviation

Calculate the median and raw median absolute deviation of a numeric sample.

You enter: Sample values

Example: Median 2; raw median absolute deviation 1.

Open Median Absolute Deviation →

Exponential Distribution

Evaluate the density, cumulative probability, survival probability, mean, and variance of an exponential waiting-time model.

You enter: Rate (lambda) · Value (x)

Example: f(2) = 0.183940; F(2) = 0.632121; survival = 0.367879; mean = 2; variance = 4.

Open Exponential Distribution →

Independent Events Probability Calculator

Find the probabilities of both, either, exactly one, or neither of two independent events.

You enter: Probability of event A · Probability of event B

Example: 10%

Open Independent Events Probability Calculator →

Combinations Calculator

Count unordered selections of r distinct items from n items without replacement.

You enter: Available items (n) · Items selected (r)

Example: 120

Open Combinations Calculator →

Normal CDF (Area Below z)

Cumulative standard-normal probability for a z-score, accurate to about 1e-7.

You enter: z-score

Example: 0.8413 (about 84.13% of values fall below z = 1).

Open Normal CDF (Area Below z) →

Binomial Probability

Exact and cumulative probabilities for a fixed number of independent trials.

You enter: Trials (n) · Successes (k) · Success probability per trial

Example: P(X = 5) = 0.2461; P(X <= 5) = 0.6230.

Open Binomial Probability →

Poisson Probability

Exact and cumulative probabilities for counted events at a known average rate.

You enter: Average rate · Events (k)

Example: P(X = 2) = 0.2240; P(X <= 2) = 0.4232.

Open Poisson Probability →

Binomial Probability Calculator

Find the probability of exactly k successes in n independent trials with a fixed success probability.

You enter: Number of trials n · Successes k · Success probability

Example: P(X = 4) ≈ 0.2051; expected value = 5; SD ≈ 1.581.

Open Binomial Probability Calculator →

Poisson Probability Calculator

Calculate the probability of exactly k events for a Poisson process with a known mean rate.

You enter: Mean event count λ · Event count k

Example: P(X = 2) ≈ 0.2240; mean = 3; variance = 3.

Open Poisson Probability Calculator →

Conditional Probability Calculator

Calculate the probability of an event given another event from their joint and conditioning probabilities.

You enter: Joint probability P(A and B) · Condition probability P(B)

Example: P(A|B) = 0.4.

Open Conditional Probability Calculator →

Birthday Collision Probability Calculator

Calculate the probability that at least two people share a birthday under a uniform-day model.

You enter: Number of people · Possible birthday days

Example: Shared-birthday probability ≈ 50.73%.

Open Birthday Collision Probability Calculator →

Six-Sided Dice Sum Probability Calculator

Calculate the exact probability of a target sum when rolling a selected number of fair six-sided dice.

You enter: Number of dice · Target sum

Example: Probability = 27/216 = 12.5%.

Open Six-Sided Dice Sum Probability Calculator →

Independent AND Probability Calculator

Calculate the probability that two independent events both occur.

You enter: Probability of event A · Probability of event B

Example: P(A and B)=0.2, or20%.

Open Independent AND Probability Calculator →

Bayes Theorem Posterior Probability Calculator

Calculate a posterior probability from prior probability, sensitivity, and specificity.

You enter: Prior probability · Sensitivity · Specificity

Example: Posterior probability ≈66.67%.

Open Bayes Theorem Posterior Probability Calculator →

Benford First-Digit Probability Calculator

Calculate the expected first-digit probability under Benford's logarithmic distribution.

You enter: First digit

Example: P(1)=log₁₀(2)≈30.10%.

Open Benford First-Digit Probability Calculator →

Binomial Exact Probability Calculator

Calculate the probability of exactly k successes in n independent Bernoulli trials.

You enter: Number of trials · Success probability · Exact successes

Example: P(X=3)≈21.47%.

Open Binomial Exact Probability Calculator →

Exact Coin-Flip Count Probability Calculator

Calculate the probability of exactly a selected number of heads in fair coin flips.

You enter: Number of flips · Exact heads

Example: Probability =252/1024≈24.61%.

Open Exact Coin-Flip Count Probability Calculator →

Normal Continuity Correction Calculator

Apply a half-unit continuity correction to a discrete count boundary and convert it to a normal z score.

You enter: Count boundary · Normal approximation mean · Normal approximation standard deviation · Event side

Example: Corrected boundary =9.5; z≈−0.8333.

Open Normal Continuity Correction Calculator →

Custom Dice Sum Probability Calculator

Calculate an exact target-sum probability for a selected number of fair dice with a selected number of sides.

You enter: Sides per die · Number of dice · Target sum

Example: Probability =8/64 =12.5%.

Open Custom Dice Sum Probability Calculator →

Beta Distribution Density Calculator

Evaluate the beta probability density and mean for a selected shape pair and value.

You enter: Alpha shape · Beta shape · Value x

Example: Density ≈2.1609; mean ≈0.2857.

Open Beta Distribution Density Calculator →

Chi-Square Goodness-of-Fit Statistic Calculator

Calculate a chi-square goodness-of-fit statistic and degrees of freedom from observed and expected counts.

You enter: Observed counts · Expected counts

Example: χ² = 2.5 with 4 degrees of freedom.

Open Chi-Square Goodness-of-Fit Statistic Calculator →

Coin Flip Streak Probability Calculator

Calculate the probability of seeing at least one run of consecutive heads in fair coin flips.

You enter: Number of flips · Heads in a row

Example: Probability of at least one three-head streak ≈50.78%.

Open Coin Flip Streak Probability Calculator →

Grouped Frequency Distribution Calculator

Group a finite numeric list into equal-width bins and count the values in each interval.

You enter: Data values · Bin width

Example: Bins [2,7): 3; [7,12): 4; [12,17): 1.

Open Grouped Frequency Distribution Calculator →

Decimal Odds Implied Probability Calculator

Convert decimal odds greater than one into implied probability and percentage.

You enter: Decimal odds

Example: Implied probability =0.4, or 40%.

Open Decimal Odds Implied Probability Calculator →

Normal Distribution Point Calculator

Calculate a z score, density, and cumulative probability for a point under a normal distribution.

You enter: Value x · Mean · Standard deviation

Example: z =1.5; density ≈0.01295; lower-tail probability ≈0.9332.

Open Normal Distribution Point Calculator →

Sample Proportion and Standard Error Calculator

Calculate a sample proportion and its simple binomial standard error from successes and trials.

You enter: Successes · Trials

Example: p̂ =0.4; standard error ≈0.04472.

Open Sample Proportion and Standard Error Calculator →

Two-Sided Normal Z P-Value Calculator

Calculate the two-sided standard-normal tail probability associated with a z statistic.

You enter: Z statistic

Example: Two-sided p-value ≈0.05.

Open Two-Sided Normal Z P-Value Calculator →

Probability to Odds Calculator

Convert a probability below one into odds in favor and log-odds.

You enter: Probability

Example: Odds =1.5; log-odds ≈0.4055.

Open Probability to Odds Calculator →

Poisson Exact Count Probability Calculator

Calculate the exact probability of observing a selected event count under a Poisson rate model.

You enter: Average event rate λ · Exact event count k

Example: P(X=2)≈0.2240.

Open Poisson Exact Count Probability Calculator →

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.

You enter: Gold-gold boxes · Gold-silver boxes · Silver-silver boxes

Example: Probability the other side is gold =2/3.

Open Bertrand Box Conditional Probability Calculator →

Boy-or-Girl Conditional Probability Calculator

Calculate the probability that both children are girls after a selected at-least-one-girl observation model.

You enter: Probability a child is a girl

Example: Probability both are girls =1/3.

Open Boy-or-Girl Conditional Probability Calculator →

Decimal Odds Probability and Payout Calculator

Convert decimal odds to implied probability and calculate total payout and net profit from a stake.

You enter: Decimal odds · Stake

Example: Implied probability =40%; payout =250; net profit =150.

Open Decimal Odds Probability and Payout Calculator →

McNemar Paired Proportion Statistic Calculator

Calculate the continuity-corrected McNemar chi-square statistic from discordant paired counts.

You enter: Discordant count b · Discordant count c

Example: Continuity-corrected chi-square ≈2.7.

Open McNemar Paired Proportion Statistic Calculator →

Monty Hall Switching Probability Calculator

Calculate stay and switch win probabilities for a generalized Monty Hall game with one prize door.

You enter: Number of doors

Example: Stay probability =33.333%; switch probability =66.667%.

Open Monty Hall Switching Probability Calculator →

Two-Game Mixed Win-Rate Calculator

Calculate the expected win probability for a random mix of two independent games.

You enter: Game A win probability · Game B win probability · Probability of selecting game A

Example: Mixed win probability =49%.

Open Two-Game Mixed Win-Rate Calculator →

Rayleigh Distribution PDF and CDF Calculator

Calculate the probability density, cumulative probability, mean, and standard deviation for a Rayleigh value.

You enter: Value x · Scale parameter σ

Example: PDF ≈0.2707; CDF ≈0.8647; mean ≈1.2533; SD ≈0.6551.

Open Rayleigh Distribution PDF and CDF Calculator →

Expected Risk and Loss Calculator

Calculate expected loss from event probability and loss amount, with the complement probability shown.

You enter: Event probability · Loss amount

Example: Expected loss =2,000; no-event probability =80%.

Open Expected Risk and Loss Calculator →

Percentile from a Data List Calculator

Estimate a percentile from a sorted or unsorted numeric list using linear interpolation between observations.

You enter: Data values · Percentile p

Example: 75th percentile =32.5; interpolated one-based position =3.25.

Open Percentile from a Data List Calculator →

Joint Probability Calculator

Calculate independent and conditional joint probabilities from event A and event B inputs.

You enter: Probability of A · Probability of B · Probability of B given A

Example: Independent joint probability = 0.20; conditional joint probability = 0.24.

Open Joint Probability Calculator →

Lognormal Distribution Calculator

Calculate lognormal density, cumulative probability, reliability, mean, and median from a median scale and shape parameter.

You enter: Median or T50 scale · Log-space shape sigma · Evaluation value

Example: CDF ≈ 0.642; PDF ≈ 0.062; mean ≈ 11.331; median = 10.

Open Lognormal Distribution Calculator →

Binomial Normal Approximation Calculator

Estimate an inclusive binomial count probability using a normal approximation with an optional continuity correction.

You enter: Number of trials · Success probability · Lower inclusive count · Upper inclusive count · Continuity correction

Example: Approximate probability for 35–45 successes is about 0.738.

Open Binomial Normal Approximation Calculator →

Sampling Distribution Probability Calculator

Calculate the probability that a sample mean falls between two bounds under a normal sampling-distribution assumption.

You enter: Population mean · Population standard deviation · Sample size · Lower mean bound · Upper mean bound

Example: Standard error = 3; probability ≈ 0.904.

Open Sampling Distribution Probability Calculator →

One-Sample Normal Power Calculator

Estimate one-sided or two-sided normal-test power from an effect, standard deviation, significance level, and sample size.

You enter: Significance level · Expected mean difference · Population standard deviation · Sample size · Alternative

Example: Noncentral shift = 2.5; approximate two-sided power ≈ 70.542%.

Open One-Sample Normal Power Calculator →

Three Independent Events Probability Calculator

Calculate the probability that three independent events all occur, at least one occurs, or none occurs.

You enter: Probability of A · Probability of B · Probability of C

Example: All three = 0.04; none = 0.24; at least one = 0.76.

Open Three Independent Events Probability Calculator →

Shannon Entropy Calculator

Calculate Shannon entropy in bits and min-entropy from a finite probability distribution.

You enter: Probabilities

Example: Shannon entropy = 1.5 bits; min-entropy = 1 bit.

Open Shannon Entropy Calculator →

Mann-Whitney U Statistic Calculator

Rank two independent samples, calculate the Mann-Whitney U statistics, and show a normal-approximation z score.

You enter: Sample A values · Sample B values

Example: Uₐ = 23; Uᵦ = 2; normal-approximation z ≈ −2.193.

Open Mann-Whitney U Statistic Calculator →

Weibull Distribution Calculator

Calculate Weibull density, cumulative probability, reliability, and mean from shape, scale, and evaluation value.

You enter: Shape parameter · Scale parameter · Evaluation value

Example: CDF ≈ 0.473; reliability ≈ 0.527; mean ≈ 8.862.

Open Weibull Distribution Calculator →

Normal Critical Value Calculator

Calculate the two-sided standard-normal critical value for an entered confidence level.

You enter: Confidence level

Example: Two-sided normal critical value ≈ 1.95996.

Open Normal Critical Value Calculator →

Moneyline Odds Calculator

Convert a positive or negative moneyline into implied probability, decimal odds, and profit on a fixed stake.

You enter: Moneyline

Example: Implied probability ≈ 52.381%; decimal odds ≈ 1.9091; profit on 100 units ≈ 90.91.

Open Moneyline Odds Calculator →

OR Probability Calculator

Calculate the probability of at least one of two events, exactly one event, and neither event from an overlap.

You enter: Probability of A · Probability of B · Probability of A and B

Example: P(A or B) = 0.70; exactly one = 0.50; neither = 0.30.

Open OR Probability Calculator →

Two-Envelope Scenario Calculator

Evaluate a transparent two-envelope switching scenario under explicit up/down ratios and a stated probability.

You enter: Amount in held envelope · Larger-envelope ratio · Smaller-envelope ratio · Probability of the larger case

Example: Expected switch value = 125; expected change = 25; break-even larger-case probability ≈ 33.33%.

Open Two-Envelope Scenario Calculator →

Fractional Odds Calculator

Convert fractional odds into decimal odds, implied probability, and profit on a fixed stake.

You enter: Profit numerator · Stake denominator

Example: Decimal odds = 3.5; implied probability ≈ 28.571%; profit on 100 units = 250.

Open Fractional Odds Calculator →

Roulette Payout and House Edge Calculator

Estimate win probability, payout, expected net result, and house edge for straight-up or even-money roulette bets.

You enter: Stake · Wheel · Bet type

Example: Win probability ≈ 2.703%; net win = 1,750; expected net ≈ −1.351; house edge ≈ 2.703%.

Open Roulette Payout and House Edge Calculator →

Sample Proportion Probability Calculator

Calculate the normal-approximation probability that a sample proportion falls between two bounds.

You enter: Population proportion · Sample size · Lower sample proportion · Upper sample proportion

Example: Proportion standard error ≈ 0.049; interval probability ≈ 0.959.

Open Sample Proportion Probability Calculator →

Two-Set Venn Count Calculator

Calculate A-only, B-only, union, overlap, and neither counts for two sets inside a stated universe.

You enter: Universe count · Set A count · Set B count · A and B overlap

Example: A-only = 50; B-only = 30; union = 100; neither = 0.

Open Two-Set Venn Count Calculator →

Combinations Without Repetition Calculator

Count how many unordered groups of a chosen size can be selected from a finite set without repeating an item.

You enter: Available items n · Items selected r

Example: There are 120 unordered groups of 3 from 10 items.

Open Combinations Without Repetition Calculator →

Probability from Favorable Outcomes

Convert favorable and total equally likely outcomes into probability, percentage, complement, and odds.

You enter: Favorable outcomes · Total equally likely outcomes

Example: Probability: 0.3; percentage: 30%; odds in favor: 3:7.

Open Probability from Favorable Outcomes →

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.

You enter: Target sum

Example: Favorable ordered outcomes: 6 of 36; probability: 1/6; percentage: 16.67%.

Open Two-Dice Sum Probability Calculator →

Histogram Bin Count Calculator

Group raw numeric values into equal-width histogram bins and report counts, relative frequencies, and density values.

You enter: Data values · Bin width · Bin origin

Example: Bins [0,2), [2,4), [4,6), [6,8), [8,10) have counts 1, 2, 2, 2, 1.

Open Histogram Bin Count Calculator →

Wilcoxon Rank-Sum Statistic

Rank two independent samples, calculate the Wilcoxon rank-sum and U statistics, and show a large-sample normal approximation.

You enter: Sample A values · Sample B values · Normal approximation correction

Example: The pooled ranks give Rₐ = 16, Uₐ = 6, expected U = 8, and z ≈ −0.577.

Open Wilcoxon Rank-Sum Statistic →

Inverse Normal Distribution Calculator

Find the normal-distribution value at a chosen cumulative percentile from a mean and standard deviation.

You enter: Mean μ · Standard deviation σ · Cumulative percentile

Example: The 95th percentile is approximately 124.6728, with z approximately 1.64485.

Open Inverse Normal Distribution Calculator →

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.

You enter: Number of flips · Heads to evaluate

Example: Exactly five heads has probability 0.24609375; at least five heads has probability 0.623046875; the expected count is 5.

Open Fair Coin Heads Probability Calculator →

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.

You enter: Numbers in the pool · Numbers selected per ticket · Numbers drawn · Minimum matches of interest · Tickets in the scenario

Example: There are 13,983,816 possible six-number draws; one fixed ticket has a jackpot chance of about 0.00000715%, or about 1 in 13,983,816.

Open Lottery Match Probability Calculator →

Inverse Standard Normal (z Quantile)

Finds the z-score with a given left-tail area under the standard normal curve.

You enter: Left-tail area

Example: z ≈ 1.9600.

Open Inverse Standard Normal (z Quantile) →

Chi-Square Goodness of Fit

Tests counts against expected counts with the Pearson chi-square statistic.

You enter: Observed counts · Expected counts

Example: χ² = 3.3333 with df = 2.

Open Chi-Square Goodness of Fit →

Bayes Flip P(A|B)

Flips P(B|A) into P(A|B) from the base rate and evidence rate.

You enter: P(B|A) · P(A) · P(B)

Example: P(A|B) = 0.18.

Open Bayes Flip P(A|B) →

Geometric Distribution

Calculate the probability that the first success occurs on a selected trial and the cumulative probability by that trial.

You enter: Success probability p · Trial of first success k

Example: P(X=3)=0.128; P(X<=3)=0.488.

Open Geometric Distribution →

Negative Binomial Distribution

Calculate the probability of observing a selected number of failures before a specified number of successes.

You enter: Required successes r · Failures before r successes k · Success probability p

Example: Probability of 2 failures before the 3rd success is 0.1875.

Open Negative Binomial Distribution →

Hypergeometric Distribution

Calculate an exact and cumulative probability for successes drawn without replacement from a finite population.

You enter: Population size (N) · Successes in population (K) · Sample size (n) · Observed successes (x)

Example: P(X = 2) = 0.476190; P(X <= 2) = 0.738095.

Open Hypergeometric Distribution →

Continuous Uniform Distribution

Evaluate the density and cumulative probability of a continuous uniform variable on a finite interval, with its mean and variance.

You enter: Lower bound (a) · Upper bound (b) · Evaluation value (x)

Example: f(4) = 0.1; F(4) = 0.4; mean = 5; variance = 8.333333.

Open Continuous Uniform Distribution →

Confidence Interval for a Mean

Two-sided z-interval for a population mean from sample mean, sd, and size.

You enter: Sample mean · Population standard deviation · Sample size · Confidence level

Example: 95% interval (95.10, 104.90); margin 4.90.

Open Confidence Interval for a Mean →

Confidence Interval for a Proportion

Wald 95/90/99% interval for a population share from successes and trials.

You enter: Successes · Trials · Confidence level

Example: 95% interval (0.5520, 0.6480); margin 0.0480.

Open Confidence Interval for a Proportion →

Sample Size for a Mean

Respondents needed to hit a margin of error at 90/95/99% confidence.

You enter: Planning standard deviation · Desired margin of error · Confidence level

Example: 217 observations.

Open Sample Size for a Mean →

Sample Size for a Proportion

Estimate how many observations a survey needs for a target proportion margin of error and confidence level.

You enter: Planning proportion · Margin of error · Confidence level · Population size (optional)

Example: 1,068 observations needed before any nonresponse adjustment.

Open Sample Size for a Proportion →

Class Width Calculator

Calculate equal histogram class width from a lower boundary, upper boundary, and number of classes.

You enter: Lower boundary · Upper boundary · Number of classes

Example: Class width = 8.

Open Class Width Calculator →

90% Mean Confidence Interval Calculator

Calculate a normal-approximation 90% confidence interval for a sample mean from standard deviation and sample size.

You enter: Sample mean · Sample standard deviation · Sample size

Example: 90% interval ≈95.89 to104.11.

Open 90% Mean Confidence Interval Calculator →

95% Mean Confidence Interval Calculator

Calculate a normal-approximation 95% confidence interval for a sample mean from standard deviation and sample size.

You enter: Sample mean · Sample standard deviation · Sample size

Example: 95% interval ≈95.10 to104.90.

Open 95% Mean Confidence Interval Calculator →

99% Mean Confidence Interval Calculator

Calculate a normal-approximation 99% confidence interval for a sample mean from standard deviation and sample size.

You enter: Sample mean · Sample standard deviation · Sample size

Example: 99% interval ≈93.56 to106.44.

Open 99% Mean Confidence Interval Calculator →

Central Limit Theorem Standard Error Calculator

Estimate the standard error and normal-approximation interval for a sample mean.

You enter: Population mean · Population standard deviation · Sample size

Example: Standard error =2; reference 95% interval =46.08 to53.92.

Open Central Limit Theorem Standard Error Calculator →

Two-Proportion A/B Test Z-Score Calculator

Compare two independent proportions with a pooled two-proportion z statistic.

You enter: Group A successes · Group A trials · Group B successes · Group B trials

Example: Group A = 12%, Group B = 15%; pooled z ≈2.02.

Open Two-Proportion A/B Test Z-Score Calculator →

One-Way ANOVA Degrees of Freedom Calculator

Calculate total, between-group, and within-group degrees of freedom from sample size and group count.

You enter: Total observations · Number of groups

Example: Total df =39, between df =3, within df =36.

Open One-Way ANOVA Degrees of Freedom Calculator →

Empirical Rule Interval Calculator

Calculate one-, two-, and three-standard-deviation intervals and their normal-model coverage percentages.

You enter: Mean · Standard deviation

Example: 1σ:85–115; 2σ:70–130; 3σ:55–145.

Open Empirical Rule Interval Calculator →

Margin of Error Calculator

Calculate a normal-approximation margin of error from a critical value, standard deviation, and sample size.

You enter: Critical value · Standard deviation · Sample size

Example: Standard error = 1.5; margin of error = 2.94.

Open Margin of Error Calculator →

Two-Sample t-Test Statistic Calculator

Calculate a two-sample t statistic using either a pooled-variance or Welch unequal-variance standard error.

You enter: Sample 1 mean · Sample 1 standard deviation · Sample 1 size · Sample 2 mean · Sample 2 standard deviation · Sample 2 size · Variance assumption

Example: Welch t ≈ 1.6855 with about 53.0 degrees of freedom.

Open Two-Sample t-Test Statistic Calculator →

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.

You enter: Sample mean · Hypothesized mean · Population standard deviation · Sample size

Example: z = 2.5; two-sided normal p-value ≈ 0.0124.

Open One-Sample z-Test Statistic Calculator →

Fisher's Exact Test Calculator

Calculate an exact two-sided Fisher probability for a 2×2 contingency table with fixed margins.

You enter: Row 1, column 1 · Row 1, column 2 · Row 2, column 1 · Row 2, column 2

Example: Observed table probability ≈ 0.2652; lower-tail p-value ≈ 0.3106; two-sided exact p-value ≈ 0.5581.

Open Fisher's Exact Test Calculator →

Mean Confidence Interval Calculator

Build a two-sided mean confidence interval from a sample mean, standard deviation, sample size, and supplied critical value.

You enter: Sample mean · Sample standard deviation · Sample size n · Two-sided critical value

Example: Standard error: 1.875; margin: 3.675; interval: 96.325 to 103.675.

Open Mean Confidence Interval Calculator →

Measurement Uncertainty Calculator

Convert an absolute measurement uncertainty into relative uncertainty, percent uncertainty, and an interval around a measured value.

You enter: Measured value · Absolute uncertainty ±

Example: Relative uncertainty: 0.04; percentage: 4%; interval: 48 to 52 units.

Open Measurement Uncertainty Calculator →

Ordering Numbers Calculator

Sort a pasted list from least to greatest and greatest to least, and report the center and endpoints.

You enter: Numbers to order

Example: Least to greatest: −1.5, 2.07, 2.7, 3.14, 10; median is 2.7.

Open Ordering Numbers Calculator →

Post-Test Probability Calculator

Use prevalence, sensitivity, and specificity to estimate positive and negative post-test probabilities with Bayes' theorem.

You enter: Pre-test prevalence · Sensitivity · Specificity

Example: Positive post-test probability is about 33.1034%; negative post-test probability of no condition is about 99.3531%.

Open Post-Test Probability Calculator →

One-Sample z Hypothesis Test Calculator

Calculate a one-sample z statistic and tail-specific p-value when the population standard deviation is supplied.

You enter: Null-hypothesis mean μ₀ · Observed sample mean · Known population standard deviation σ · Sample size n · Significance level α · Alternative hypothesis

Example: z ≈ 11.1803, the right-tail p-value is effectively 0%, and the null is rejected at 5% in this model.

Open One-Sample z Hypothesis Test Calculator →

Confidence Interval for a Mean (t)

t-interval for the mean when sigma is unknown.

You enter: Sample mean · Sample standard deviation · Sample size · Confidence level

Example: df 15, t* 2.131, margin 7.991; interval (92.009, 107.991).

Open Confidence Interval for a Mean (t) →

Bonferroni Correction

Calculate a Bonferroni-adjusted significance threshold and adjusted p-value for multiple comparisons.

You enter: Unadjusted alpha · Number of comparisons · Observed p-value

Example: Adjusted alpha 0.01; adjusted p-value 0.05.

Open Bonferroni Correction →

Correlation Coefficient (r)

Pearson correlation between two equal-length numeric lists.

You enter: x values · y values

Example: r = 1 (perfect positive linear association).

Open Correlation Coefficient (r) →

Least-Squares Regression Line

Slope, intercept, and fitted equation for paired data.

You enter: x values · y values

Example: y-hat = 1 + 2x.

Open Least-Squares Regression Line →

Coefficient of Determination Calculator

Square a correlation coefficient to express the proportion of linear variation represented by the fitted relationship.

You enter: Correlation coefficient r

Example: R² = 0.64, or 64%.

Open Coefficient of Determination Calculator →

Cubic Prediction Polynomial Calculator

Evaluate a cubic prediction equation from four supplied coefficients and an input x value.

You enter: Input x · Coefficient a · Coefficient b · Coefficient c · Intercept d

Example: Predicted y =4.

Open Cubic Prediction Polynomial Calculator →

Matthews Correlation Coefficient Calculator

Calculate the Matthews correlation coefficient from binary-classification confusion counts.

You enter: True positives · True negatives · False positives · False negatives

Example: Matthews correlation coefficient ≈0.7035.

Open Matthews Correlation Coefficient Calculator →

Prediction Residual Calculator

Calculate signed residual, absolute residual, and squared residual from observed and predicted values.

You enter: Observed value · Predicted value

Example: Residual =2; absolute residual =2; squared residual =4.

Open Prediction Residual Calculator →

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.

You enter: Exposed cases a · Exposed non-cases b · Unexposed cases c · Unexposed non-cases d

Example: Odds ratio =2.5; log odds ratio ≈0.9163.

Open Odds Ratio from a Two-by-Two Table Calculator →

Quadratic Regression Calculator

Fit a least-squares quadratic y=a+bx+cx² to paired data and evaluate the fitted equation at a target x.

You enter: X values · Y values · Target x

Example: Fit is y=1+1x+1x²; predicted y at x=5 is 31; R² = 1.

Open Quadratic Regression Calculator →

Population Skewness Calculator

Calculate the Fisher-Pearson population skewness of a finite list of observations.

You enter: Data values

Example: Population skewness ≈ 1.361.

Open Population Skewness Calculator →

Quartic Regression Calculator

Fit a fourth-degree least-squares polynomial to paired data and evaluate it at a target value.

You enter: X values · Y values · Target x

Example: Fit is approximately y=x⁴; predicted y at x=4 is 256; R² = 1.

Open Quartic Regression Calculator →

Least-Squares Linear Regression Calculator

Fit a straight line to paired observations and report the slope, intercept, prediction, correlation, and explained variation.

You enter: X values · Y values · Prediction x

Example: The fitted line is ŷ = −0.2 + 2x; at x = 6 it predicts 11.8, with R² ≈ 0.9804.

Open Least-Squares Linear Regression Calculator →

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.

You enter: x values · Matching y values · x value to predict

Example: The fitted line is approximately y = 2x − 0.4 and predicts about 11.6 at x = 6.

Open Scatter Plot and Linear Regression Calculator →

Pearson Correlation Calculator

Calculate Pearson’s r, r², means, and supporting sums from paired X and Y observations entered as comma-separated values.

You enter: X values · Y values

Example: The paired data have r ≈ 0.870 and r² ≈ 0.758.

Open Pearson Correlation Calculator →

Polynomial Regression Calculator

Fit an ordinary least-squares polynomial of degree 1 to 5 to paired observations and report the equation, R², and RMSE.

You enter: X values · Y values · Polynomial degree

Example: The exact quadratic fit is y = 1 + 1x + 1x² with R² = 1 and RMSE = 0.

Open Polynomial Regression Calculator →

Spearman Rank Correlation

Calculate Spearman's rank correlation for two paired data sets, including average ranks for ties.

You enter: X values · Y values

Example: Spearman rank correlation is -0.4.

Open Spearman Rank Correlation →

Classification Accuracy Calculator

Calculate accuracy from correct classifications and total evaluated cases.

You enter: Correct classifications · Total classifications

Example: Accuracy =92%.

Open Classification Accuracy Calculator →

Confusion Matrix Metrics Calculator

Calculate accuracy, precision, recall, specificity, and F1 score from a binary confusion matrix.

You enter: True positives · True negatives · False positives · False negatives

Example: Accuracy =85%; precision ≈88.89%; recall =80%; specificity =90%; F1≈84.21%.

Open Confusion Matrix Metrics Calculator →

False Positive and Predictive Value Calculator

Calculate false-positive rate, positive predictive value, and false discovery rate from prevalence, sensitivity, and specificity.

You enter: Prevalence · Sensitivity · Specificity

Example: False-positive rate =5%; PPV ≈66.667%; false discovery rate ≈33.333%.

Open False Positive and Predictive Value Calculator →

Process Capability Cp and Cpk Calculator

Calculate Cp and Cpk from specification limits, process mean, and process standard deviation.

You enter: Lower specification limit · Upper specification limit · Process mean · Process standard deviation

Example: Cp ≈1.6667; Cpk ≈1.6667.

Open Process Capability Cp and Cpk Calculator →

Youden's J Index Calculator

Calculate Youden's J from sensitivity and specificity for a binary classification threshold.

You enter: Sensitivity · Specificity

Example: Youden J = 0.75, or 75 percentage points.

Open Youden's J Index Calculator →

False Positive Base-Rate Calculator

Calculate positive predictive value and negative predictive value from prevalence, sensitivity, and false-positive rate.

You enter: Prevalence · Sensitivity · False-positive rate

Example: PPV ≈ 15.38%; NPV ≈ 99.90%.

Open False Positive Base-Rate Calculator →

Sensitivity Calculator

Calculate sensitivity, miss rate, and the number of actual positive cases from true positives and false negatives.

You enter: True positives · False negatives

Example: Sensitivity: 90%; miss rate: 10%; actual positives: 100.

Open Sensitivity Calculator →

Specificity Calculator

Calculate specificity, false-positive rate, and the number of actual negative cases from true negatives and false positives.

You enter: True negatives · False positives

Example: Specificity: 90%; false-positive rate: 10%; actual negatives: 200.

Open Specificity Calculator →

Sensitivity and Specificity Calculator

Summarize all four cells of a binary classification table with sensitivity, specificity, accuracy, and prevalence.

You enter: True positives · False negatives · True negatives · False positives

Example: Sensitivity: 90%; specificity: 90%; accuracy: 90%; prevalence: 30%.

Open Sensitivity and Specificity Calculator →

Permutations Calculator

Count ordered arrangements of r distinct items chosen from n.

You enter: Available items (n) · Items arranged (r)

Example: 720

Open Permutations Calculator →

Moving Average Calculator

Calculate simple moving averages from a comma-separated sequence and a selected window size.

You enter: Sequence values · Window size

Example: Moving averages = 12, 14, 16; latest = 16.

Open Moving Average Calculator →

Acceptance Rate Calculator

Calculate acceptance and rejection percentages from the number accepted and the total number of applications or trials.

You enter: Accepted cases · Total cases

Example: Acceptance = 24%; rejection = 76%.

Open Acceptance Rate Calculator →

Absolute and Relative Uncertainty Calculator

Calculate relative and percentage uncertainty from a measured value and an absolute uncertainty.

You enter: Measured value · Absolute uncertainty

Example: Relative uncertainty =0.04; percentage uncertainty =4%.

Open Absolute and Relative Uncertainty Calculator →

Ascending Numeric Order Calculator

Parse a short comma- or space-separated list of numbers and return it in ascending order.

You enter: Numbers

Example: Ascending order =2, 2, 4, 7, 9.

Open Ascending Numeric Order Calculator →

Decile from Numeric Data Calculator

Estimate a selected decile from a numeric list using linear interpolation of the sorted positions.

You enter: Data values · Decile number

Example: Fifth decile =17.5 under the stated interpolation convention.

Open Decile from Numeric Data Calculator →

Independent Measurement Error Propagation Calculator

Estimate propagated absolute uncertainty for addition, subtraction, multiplication, or division of two measured values.

You enter: Operation · Value A · Absolute uncertainty A · Value B · Absolute uncertainty B

Example: Result =16; propagated uncertainty ≈0.361.

Open Independent Measurement Error Propagation Calculator →

First Quartile Calculator

Calculate the 25th percentile from a finite numeric list using linear interpolation on sorted positions.

You enter: Data values

Example: Q1 =4.5.

Open First Quartile Calculator →

IQR Outlier Fence Calculator

Calculate Tukey outlier fences and classify one value using first and third quartiles.

You enter: Value to classify · First quartile Q1 · Third quartile Q3

Example: IQR =8; upper fence =24; 18 is not an outlier.

Open IQR Outlier Fence Calculator →

Relative and Percentage Error Calculator

Calculate signed relative error and absolute percentage error from an actual value and a nonzero reference.

You enter: Measured or estimated value · Reference value

Example: Relative error =−0.02; absolute percentage error =2%.

Open Relative and Percentage Error Calculator →

Index of Qualitative Variation Calculator

Calculate the index of qualitative variation from category counts.

You enter: Category counts

Example: Index of qualitative variation ≈0.93.

Open Index of Qualitative Variation Calculator →

Lower Outlier Fence Calculator

Calculate interquartile range and the lower Tukey outlier fence from first and third quartiles.

You enter: First quartile Q1 · Third quartile Q3

Example: IQR =8; lower fence =−2.

Open Lower Outlier Fence Calculator →

Proportion Point Estimate Calculator

Calculate a sample proportion point estimate and its complement from successes and trials.

You enter: Successes · Trials

Example: Point estimate =42%; complement =58%.

Open Proportion Point Estimate Calculator →

Sampling Error Difference Calculator

Calculate the signed sampling error between a sample proportion and a supplied population proportion.

You enter: Sample proportion · Reference population proportion

Example: Signed sampling error =−0.04; absolute error =0.04.

Open Sampling Error Difference Calculator →

Interquartile Range Calculator

Calculate the interquartile range and midhinge from supplied first and third quartiles.

You enter: First quartile Q1 · Third quartile Q3

Example: IQR =16; midhinge =20.

Open Interquartile Range Calculator →

Upper Tukey Fence Calculator

Calculate the upper exploratory fence from first and third quartiles using the 1.5-IQR convention.

You enter: First quartile Q1 · Third quartile Q3

Example: IQR =16; upper fence =52.

Open Upper Tukey Fence Calculator →

Percentile Rank Calculator

Estimate the percentile rank of a target value within a numeric data list, including a transparent tie convention.

You enter: Data values · Target value

Example: Percentile rank =70%.

Open Percentile Rank Calculator →

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.

You enter: Exposed cases a · Exposed non-cases b · Unexposed cases c · Unexposed non-cases d

Example: Exposed risk =33.33%; unexposed risk =16.67%; relative risk =2.

Open Relative Risk from a Two-by-Two Table Calculator →

Pooled Two-Sample Degrees of Freedom Calculator

Calculate the pooled degrees of freedom for an independent two-sample comparison.

You enter: Group 1 sample size · Group 2 sample size

Example: Pooled degrees of freedom =36.

Open Pooled Two-Sample Degrees of Freedom Calculator →

Independent Sum Error Propagation Calculator

Calculate the combined absolute and relative uncertainty for a sum or difference of two measured quantities.

You enter: Value 1 · Uncertainty 1 · Value 2 · Uncertainty 2

Example: Combined value =20; absolute uncertainty ≈0.5; relative uncertainty =2.5%.

Open Independent Sum Error Propagation Calculator →

Relative Frequency Calculator

Convert an observed count into a relative frequency, percentage, and complement within a stated total.

You enter: Observed count · Total count

Example: Relative frequency = 0.4; percentage = 40%; complement = 60%.

Open Relative Frequency Calculator →

Simpson Diversity Index Calculator

Calculate Simpson concentration and Gini-Simpson diversity from category counts.

You enter: Category counts

Example: Simpson concentration D ≈ 0.3737; Gini-Simpson diversity ≈ 0.6263.

Open Simpson Diversity Index Calculator →

Midrange Calculator

Calculate the minimum, maximum, range, and midrange of a numeric data list.

You enter: Data values

Example: Minimum = 4; maximum = 20; midrange = 12; range = 16.

Open Midrange Calculator →

Pie Chart Angle Calculator

Convert a category count within a total into a percentage and the central angle for a pie-chart slice.

You enter: Category count · Total count

Example: Share = 25%; pie angle = 90° = π/2 radians.

Open Pie Chart Angle Calculator →

Range Calculator

Calculate the minimum, maximum, and total range of a numeric data list.

You enter: Data values

Example: Minimum = 12; maximum = 30; range = 18.

Open Range Calculator →

Range and Relative Dispersion Calculator

Calculate the range, midrange, and coefficient of range from a positive minimum and maximum.

You enter: Minimum value · Maximum value

Example: Range: 12; midrange: 16; coefficient of range: 0.375.

Open Range and Relative Dispersion Calculator →

Interquartile Spread (IQR) Calculator

Find the interquartile range, midhinge, and quartile spread from the first and third quartiles.

You enter: First quartile Q1 · Third quartile Q3

Example: IQR: 16; midhinge: 20; quartile coefficient: 0.40.

Open Interquartile Spread (IQR) Calculator →

Minimum, Maximum, and Range Calculator

Calculate the span, midpoint, and endpoint ratio from a minimum and maximum observation.

You enter: Minimum value · Maximum value

Example: Range: 12; midpoint: 14; maximum/minimum ratio: 2.5.

Open Minimum, Maximum, and Range Calculator →

Permutation Calculator

Count ordered selections of r distinct items from n available items without repetition.

You enter: Available items n · Positions filled r

Example: There are 720 ordered selections of 3 from 10 items.

Open Permutation Calculator →

Upper and Lower Outlier Fence Calculator

Calculate the lower and upper Tukey-style outlier fences from Q1, Q3, and an entered IQR multiplier.

You enter: First quartile Q1 · Third quartile Q3 · IQR multiplier

Example: IQR is 12; the lower fence is −11 and the upper fence is 37.

Open Upper and Lower Outlier Fence Calculator →

Stem-and-Leaf Plot Calculator

Sort raw values into a text stem-and-leaf display while retaining the individual observations.

You enter: Data values · Leaf unit represented by one leaf

Example: The stems are 1 | 2 4 5 7 and 2 | 1 2 4 8.

Open Stem-and-Leaf Plot Calculator →

Dot Plot Frequency Table Calculator

Count repeated values in a raw dataset and produce a sorted dot-plot table with frequencies and proportions.

You enter: Data values

Example: Value 3 has 3 dots (37.5%); the total number of observations is 8.

Open Dot Plot Frequency Table Calculator →

Pie Chart Percentage Calculator

Calculate a category's share, percentage, and pie-slice angle from a category count and total count.

You enter: Category count · Total count

Example: Share is 0.3, percentage is 30%, and the pie-slice angle is 108°.

Open Pie Chart Percentage Calculator →

Password Combination Calculator

Count the exact number of passwords possible from an alphabet size and length, with or without character reuse.

You enter: Available characters · Password length · May a character repeat?

Example: 62¹² = 3,226,266,762,397,899,821,056 possible strings, an approximately 71.45-bit search space.

Open Password Combination Calculator →

Pie Chart Slice Calculator

Turn a list of category values into totals, percentages, and central angles for a complete pie chart.

You enter: Category values

Example: The total is 100; the slices are 25%/90°, 35%/126°, and 40%/144° in input order.

Open Pie Chart Slice Calculator →

Exponential Growth and Decay Calculator

Project a positive starting value under discrete compounding or continuous exponential growth and display the change and doubling time.

You enter: Initial value · Rate per time unit · Elapsed time · Growth model · Compounding periods per time unit

Example: The final value is about 1,628.895, a growth factor of 1.628895, after ten annual periods.

Open Exponential Growth and Decay Calculator →

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.

You enter: Reference-group earnings · Comparison-group earnings

Example: The unadjusted gap is 10%; the comparison group earns 90% of the reference-group amount, a difference of 500 pay units.

Open Gender Pay Gap Percentage Calculator →

Combinations With Repetition

Count unordered selections of a fixed size from reusable types, where selecting the same type more than once is allowed.

You enter: Available types (n) · Selections (r)

Example: 35 unordered selections of 3 items from 5 reusable types.

Open Combinations With Repetition →

Permutations With Repetition

Count ordered sequences of a fixed length from reusable types, where each position may use any type again.

You enter: Available types (n) · Sequence length (r)

Example: 125 ordered sequences of length 3 from 5 reusable types.

Open Permutations With Repetition →