Math and learning toolkit

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.

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.

Weighted Grade Calculator Combine component percentage scores with relative weights and inspect each contribution to the overall grade. Credit-Weighted 4.0 GPA Calculator Calculate GPA from numeric grade points and matching course credits, with a quality-points breakdown. Required Final Exam Grade Calculator Find the final exam score needed for a target course grade and identify impossible or already-secured targets. Reading Time Calculator Estimate reading duration from a word count and your own reading speed, with a rounded planning allowance. Reading Challenge Pace Calculator Calculate planned pages per day and total planned pages for a reading challenge with an optional buffer. Additive Grade Curve Calculator Apply a clearly stated additive class-average shift to a raw score, with an explicit score cap and both capped and uncapped results. IELTS Overall Band Score Calculator Calculate the overall IELTS band from Listening, Reading, Writing, and Speaking section bands using the official half-band rounding rule. ACT Composite Score Calculator Calculate the current ACT Composite from English, Math, and Reading section scores, with a separate Science and STEM view. Ability Score Point-Buy Planner Plan six ability scores with a transparent 27-point cost table, remaining budget, and derived modifiers. Semester Grade Target Planner Calculate the current weighted contribution, required score on remaining work, and best possible final grade for a semester target.