Math calculator glossary: formulas, methods & concepts

Absolute Value determines absolute value of a number or expression, solves absolute-value equations and inequalities, and calculates the distance between two numbers.

An annulus is the ring-shaped geometric region bounded by two concentric circles, calculated from outer and inner radii to determine surface area, perimeter, and radial width.

Free one-way ANOVA calculator — F-statistic, p-value, critical F, eta-squared effect size, and pairwise post-hoc comparisons across 3-4 groups.

Arc Length calculates arc length and sector area of a circle from the radius and central angle, with solutions for radius or angle.

Area & Perimeter calculates area and perimeter of rectangles and squares.

Arithmetic Sequence determines nth term and the sum of an arithmetic sequence from the first term and common difference, with the term list.

Average calculates average (arithmetic mean) of a list of numbers, plus the sum, count, min, max, and range.

Bayes' Theorem calculates posterior probability P(A|B) using Bayes' theorem from the prior, likelihood, and evidence, with a medical-test example mode.

Binomial Distribution calculates binomial probabilities — exactly, at most, or at least k successes — from the number of trials and success probability, with mean and SD.

Perform bitwise operations — AND, OR, XOR, NOT, and left/right shifts — on two integers, with binary, decimal, and hex output.

Box Plot generates a box-and-whisker plot from a data set, with the five-number summary, IQR, whiskers, and outliers.

Central Limit Theorem calculates mean and standard error of a sampling distribution using the central limit theorem, and the probability of a sample mean range.

Run a chi-square goodness-of-fit or test of independence from observed and expected counts, with the statistic, degrees of freedom, and p-value.

Chord Length calculates length of a chord in a circle from the radius and central angle, or from the radius and distance from the center.

Circle calculates circle area, circumference, and diameter.

Circular Segment calculates area, arc length, chord, and height of a circular segment from the radius and central angle (or chord and height).

Coefficient of Variation calculates coefficient of variation (relative standard deviation) from a data set or from a mean and standard deviation.

A matrix determinant via cofactor (Laplace) expansion along a chosen row or column, with every minor shown.

Collatz Conjecture generates the Collatz sequence (3n+1 problem) for any starting number, with the number of steps and the peak value reached.

Completing the Square converts a quadratic ax² + bx + c into vertex form a(x − h)² + k by completing the square, with the vertex and the steps.

Add, subtract, multiply, and divide complex numbers, and finds modulus, argument, conjugate, polar form, powers, and roots.

Concentration & Dilution calculates molarity, moles, and C1V1=C2V2 dilutions, plus serial dilution planning.

Conditional Probability calculates conditional probability P(A|B) from the joint probability and P(B), or from event counts, with an independence check.

A cone is a three-dimensional geometric body that tapers smoothly from a flat circular base to an apex point.

Confidence Interval calculates confidence intervals for means and proportions.

A continued fraction rewrites a number as a nested stack of integer divisions, [a0; a1, a2, ...].

Correlation Coefficient calculates Pearson r and linear regression stats.

Covariance calculates covariance between two variables (population or sample) from paired data, with the means and the correlation coefficient.

Critical Value determines critical value for a z, t, chi-square, or F distribution from the significance level and degrees of freedom, for hypothesis testing.

The cross product takes two 3D vectors, a and b, and returns a new vector perpendicular to both.

Cube calculates volume, surface area, face diagonal, and space diagonal of a cube from its edge length, or solve backward.

Cubic Equation solves for a cubic equation ax³ + bx² + cx + d = 0 for all real and complex roots, with the discriminant and nature of the roots.

A cylinder is a three-dimensional geometric solid with two parallel congruent circular bases connected by a smooth curved lateral surface.

Degrees of Freedom calculates degrees of freedom for a one-sample, two-sample, paired t-test, chi-square, or ANOVA from the sample sizes.

Derivative calculates derivatives of common functions analytically or numerically — shows formula, tangent line equation, step-by-step work, and interactive curve visualization.

Diagonal calculates diagonal of a rectangle, square, or box, and the number of diagonals in a polygon, from the dimensions.

Dice Probability computes dice roll probabilities for TTRPGs: sum distributions, at-least/at-most odds, advantage/disadvantage, and modifiers for any dice pool.

Distance Between Points calculates distance and midpoint between two points.

The dot product is one of the most useful operations in vector algebra: it turns two vectors into a single number that.

Double Angle calculates sin(2θ), cos(2θ), and tan(2θ) using the double-angle identities from an angle or from sin/cos of θ.

Effect Size calculates Cohen's d effect size from two group means and standard deviations, with the pooled SD and a small/medium/large interpretation.

Eigenvalue calculates eigenvalues and eigenvectors of a 2×2 or 3×3 matrix from the characteristic polynomial.

An ellipse is a smooth closed geometric curve where the sum of the distances from any point on the boundary to two fixed focal points is constant.

Apply the empirical rule (68-95-99.7) to a normal distribution from the mean and standard deviation, and finds the range for 1, 2, or 3 standard deviations.

Euler's totient function, written φ(n), counts how many positive integers up to n share no common factor with n.

Expected Value calculates expected value for probability distributions.

Exponent calculates powers, roots, and fractional exponents with step-by-step explanations.

Exponential Distribution calculates exponential distribution probabilities and the mean, median, and variance from the rate parameter, for waiting-time problems.

Exponential Growth models exponential growth or decay from an initial value, rate, and time, and solve for the rate, time, or doubling/half-life.

Run an F-test to compare the variances of two samples, giving the F-statistic, degrees of freedom, and p-value.

Factorial calculates factorial of a number (n!), including large values, with the expansion and use in permutations and combinations.

List all factors (divisors) of a number, count them, sum them, and show the factor pairs and whether the number is prime, perfect, or abundant.

Fibonacci determines nth Fibonacci number exactly with BigInt, list the sequence with its running sum, and watch the ratio converge to the golden ratio.

Visualize Fourier series approximations for square, sawtooth, and triangle waves with animated harmonic decomposition.

A numerical quantity representing a part of a whole, written as a numerator over a denominator (e.g., 3/4). Operations include addition, subtraction, multiplication, and division.

Build a frequency distribution table from raw data — frequency, relative frequency, and cumulative frequency — with a chosen class width.

Frustum calculates volume, slant height, and surface area of a conical frustum (truncated cone) from its two radii and height.

GCF and LCM determines greatest common factor (GCF/GCD) and least common multiple (LCM) of two or more numbers, with the prime factorization and step-by-step method.

Geometric Distribution calculates geometric distribution probabilities — the trial of the first success — from the success probability, with mean and cumulative odds.

Geometric Mean calculates geometric mean of a set of positive numbers, useful for growth rates and ratios, with the arithmetic mean for comparison.

Split a length into the golden ratio (φ ≈ 1.618), or find the longer or shorter segment and the golden-rectangle dimensions.

A numerical representation of a student's academic performance calculated by averaging grade points across courses, often weighted by credit hours. Typically uses a 4.0 scale in the U.S.

Great-Circle Distance computes great-circle (as-the-crow-flies) distance between two latitude/longitude points using the haversine formula, plus initial bearing.

Harmonic Mean calculates harmonic mean of a set of numbers, useful for averaging rates and speeds, with arithmetic and geometric means for comparison.

Hemisphere calculates volume, curved surface area, and total surface area of a hemisphere from its radius, or solve backward.

Heron's Formula calculates area of a triangle from its three side lengths using Heron's formula, with the semi-perimeter and a validity check.

Hypergeometric Distribution calculates hypergeometric probabilities — drawing without replacement — from population size, successes, sample size, and observed successes.

Run t-tests and chi-square tests from raw sample data — one-sample, two-sample, paired, and chi-square.

Integral estimates definite integrals numerically with Trapezoidal, Midpoint, and Simpson's Rule — includes exact values, error estimates, and Riemann visualization.

Kite calculates area and perimeter of a kite from its diagonals or its two pairs of sides and angle.

Law of Cosines solves for a triangle with the law of cosines (c² = a² + b² − 2ab·cosC) for a side or angle from SAS or SSS.

Law of Sines solves for a triangle with the law of sines (a/sinA = b/sinB = c/sinC) from an angle-side pair plus one more value, with the ambiguous-case check.

Line Equation determines equation of a line from two points or a point and slope, in slope-intercept, point-slope, and standard form, with slope and intercepts.

Linear Interpolation estimates unknown value between two known points with linear interpolation, or extrapolate beyond them.

Free linear regression calculator — slope, y-intercept, R-squared, correlation, standard error, p-value, and predicted Y with residual analysis.

Logarithm calculates log base 10, natural log, log base 2, or any custom base with step-by-step work.

Divide numbers with full step-by-step long division — quotient, remainder, and decimal expansion shown the way it's taught.

Multiply two numbers using the long multiplication (standard algorithm) method, showing each partial product and the worked steps.

LU decomposition rewrites a square matrix A as the product of a lower-triangular matrix L and an upper-triangular.

Run a Mann-Whitney U test (Wilcoxon rank-sum) to compare two independent groups without assuming normality, with the U statistic and z/p-value.

Margin of Error calculates margin of error for a survey proportion or mean from sample size, confidence level, and variability, with the confidence interval.

Add, multiply, finds determinants, inverses, and solve systems of equations with step-by-step solutions.

Matrix Determinant calculates determinant of a 2×2, 3×3, or 4×4 matrix, with the cofactor-expansion steps and a singular/invertible check.

Matrix Inverse calculates inverse of a 2×2 or 3×3 matrix using the adjugate method, with the determinant and a verification (A·A⁻¹ = I).

Multiply two matrices of compatible dimensions (A × B), with the row-by-column dot-product steps shown.

The rank of a matrix using row-echelon reduction (Gaussian elimination), showing linearly independent rows.

The trace is one of the simplest numbers you can compute from a square matrix.

The transpose of a matrix (Aᵀ), flipping rows and columns, with a symmetric-matrix check.

Mean Absolute Deviation calculates mean absolute deviation (MAD) of a data set about the mean or median, with the deviations table.

Mean Median Mode calculates mean, median, mode, and range for any data set.

Mean Squared Error calculates mean squared error (MSE) and root mean squared error (RMSE) between predicted and actual values, for regression and forecasting.

Midpoint determines midpoint between two coordinate points, plus the distance and slope of the line segment joining them.

Midrange calculates midrange of a data set — the average of the maximum and minimum — plus the range, mean, and median for comparison.

Add, subtract, multiply, and divide mixed numbers and improper fractions, with a fully simplified result and the steps.

A^b mod m efficiently using fast square-and-multiply exponentiation, with BigInt support.

Modulo calculates mod n and see the remainder under the truncated, floored, and Euclidean sign conventions, plus the quotient and modular exponentiation.

Molar Mass calculates molar mass of any chemical compound, view element percent composition, and converts between mass and moles.

Normal Distribution calculates probabilities for normal distribution curves.

Octahedron calculates volume, surface area, and insphere/circumsphere radii of a regular octahedron from its edge length.

Odds Ratio calculates odds ratio and relative risk from a 2×2 contingency table, with confidence intervals, for study and epidemiology data.

Evaluate an expression step by step following PEMDAS/BODMAS order of operations, showing each stage of the simplification.

Identify outliers in a data set using the IQR (1.5x) fences and the z-score method, with the cleaned data set.

P-Value determines statistical significance with p-value analysis.

Parallelogram calculates area, perimeter, height, and diagonals of a parallelogram from its base, side, height, or angle.

Decompose a rational expression into partial fractions, handling distinct linear, repeated, and irreducible quadratic factors.

Pascal's Triangle generates Pascal's triangle to any number of rows, look up a binomial coefficient (n choose k), and see the row sums.

Percent Error calculates percent error between a measured (experimental) value and the true (accepted) value, with absolute and relative error.

A fraction expressed as a portion of 100. Used in calculations for discounts, interest rates, tax, tips, grades, and statistical analysis.

Percentage Change calculates percentage increase or decrease between two numbers, plus percentage difference and the new value after a percent change.

Percentile determines value at a given percentile in a data set, or the percentile rank of a value, with a choice of interpolation method.

Permutation & Combination calculates nPr and nCr with step-by-step factorial work and Pascal's Triangle.

Point Estimate calculates best point estimate of a population proportion from the number of successes and trials, using MLE, Wilson, Laplace, and Jeffrey methods.

Poisson Distribution calculates Poisson probabilities — exactly k, at most k, or at least k events — from the average rate λ, with the distribution table.

Polygon Area calculates area of regular and irregular polygons from side lengths or coordinates.

Pooled Variance calculates pooled variance and pooled standard deviation of two or more groups from their variances and sample sizes.

Prime Factorization determines prime factors, check primality, and computes GCD and LCM with step-by-step work.

Prime Number evaluates whether a number is prime, finds its prime factorization, and lists primes in a range using the Sieve of Eratosthenes.

Probability calculates probability, binomial distributions, nCr, nPr, and expected value with step-by-step solutions and simulation.

Pyramid calculates volume, surface area, and slant height of a rectangular or square pyramid from its base and height.

The Pythagorean Theorem is a geometric principle stating that in any right triangle, the square of the hypotenuse equals the sum of the squares of the other two legs (a² + b² = c²).

Pythagorean Triples generates Pythagorean triples from Euclid's formula, check whether three numbers form a triple, or list all triples with a leg or hypotenuse.

The quadratic formula calculates the roots or x-intercepts of any second-degree polynomial equation (ax² + bx + c = 0) from its numerical coefficients.

Quartile determines quartiles (Q1, Q2, Q3), interquartile range, and outliers of a data set, with the five-number summary.

R-Squared calculates coefficient of determination (R²) from paired data or from the correlation coefficient, with the explained-variance interpretation.

Radians to Degrees converts radians and degrees (and gradians), with exact multiples of π for common angles.

Random Number Generator generates random numbers in any range, pick multiple at once with or without duplicates, and sort the results. Includes dice, coin flip, and lottery quick-pick modes.

Ratio simplifies ratios, solves proportions (A:B = C:x), scales ratios up or down, and converts a ratio to a fraction, decimal, or percentage.

Rectangular Prism calculates volume, surface area, and space diagonal of a rectangular prism (box) from its length, width, and height.

Regular Polygon calculates area, perimeter, interior and exterior angles, and apothem of a regular polygon from its number of sides and side length.

Relative Frequency calculates relative frequency and cumulative relative frequency of each category or class from raw counts, as fractions and percentages.

A rhombus is a four-sided equilateral parallelogram whose opposite angles are equal and whose diagonals bisect each other at perpendicular right angles.

Right Triangle solves for a right triangle from any two known values — legs, hypotenuse, or an angle — using the Pythagorean theorem and trigonometry.

Root calculates square root, cube root, or any nth root of a number, and solve the inverse (x^n) with real and negative-base handling.

Round a number to a chosen decimal place, significant figures, or nearest 10/100/1000, with several rounding methods.

Sample Size calculates required sample size for surveys and experiments.

The scalar triple product a·(b×c) combines the cross product and the dot product into a single number that measures how.

A full scientific calculator with trig, logarithms, exponents, factorials, and memory functions, right in browser.

Scientific Notation converts numbers to/from scientific notation and operate on them.

Section Formula determines point that divides a line segment in a given ratio (internal or external division) using the section formula.

Sensitivity and Specificity calculates sensitivity, specificity, PPV, NPV, and accuracy of a diagnostic test from true/false positives and negatives.

Sequence & Series calculates nth term, partial sums, and series convergence for arithmetic, geometric, and Fibonacci sequences.

Set Theory computes union, intersection, difference, symmetric difference, and Cartesian product of two sets, plus subset checks and cardinality.

Count sig figs, round to N significant figures, and apply sig fig rules to arithmetic.

Skewness and Kurtosis calculates skewness and kurtosis of a data set to describe the shape of its distribution, with a plain-language reading.

Slope calculates slope, y-intercept, and line equation from points.

Spearman's Correlation calculates Spearman's rank correlation coefficient (rho) from paired data, for monotonic relationships, with a strength interpretation.

A sphere is a perfectly symmetrical three-dimensional geometric shape where every point on the surface is equidistant from a common center point.

Spherical Cap calculates volume and surface area of a spherical cap (dome) from the sphere radius and cap height, useful for tank and dome volumes.

Standard deviation measures the dispersion or spread of values in a dataset relative to its statistical mean, quantifying data variability in the same units as the original observations.

Standard Error calculates standard error of the mean from a data set or from a standard deviation and sample size (SE = SD/√n).

Statistical Power calculates statistical power of a test, or the sample size needed for a target power, from the effect size, significance level, and sample size.

Mean, median, mode, SD, variance, quartiles, skewness, kurtosis, confidence interval, and z-scores from any dataset.

Sum of Squares calculates total sum of squares (SS) of a data set — the sum of squared deviations from the mean — plus the mean and variance.

Evaluate a summation (sigma notation) of an expression over an index range, with the terms and running total.

Surface Area calculates surface area of cubes, spheres, cylinders, cones, and pyramids.

Divide a polynomial by a linear factor (x − c) using synthetic division, showing the quotient, remainder, and the worked table.

System of Equations solves for 2×2 and 3×3 systems of linear equations with exact fractions, step-by-step elimination, and Cramer's rule.

Run a one-sample, two-sample, or paired t-test from summary statistics, with the t-statistic, degrees of freedom, and p-value.

Tetrahedron calculates volume, surface area, height, and face area of a regular tetrahedron from its edge length.

Torus calculates volume and surface area of a torus (donut) from its major and minor radii.

A trapezoid is a four-sided convex quadrilateral with at least one pair of parallel opposite sides, evaluated using its base lengths and vertical height.

Triangle calculates triangle area, sides, and angles from inputs.

A triangular prism is a three-dimensional polyhedron bounded by two parallel congruent triangular bases and three rectangular lateral faces.

Trigonometry calculates sine, cosine, tangent, and their reciprocals and inverses for any angle in degrees or radians.

Truth Table Generator generates the truth table for a logical expression with AND, OR, NOT, XOR, implication, and biconditional, and identify tautologies and contradictions.

Unit Circle determines coordinates (cos, sin) on the unit circle for any angle, the reference angle, and the quadrant, in degrees or radians.

Variance calculates variance of a data set (population or sample), plus the mean, sum of squares, and standard deviation.

Add, subtract, and scale 2D or 3D vectors, and computes magnitude, dot product, cross product, and the angle between vectors.

Vector projection splits a vector a into two pieces relative to a second vector b: the part of a that points along b.

Volume calculates volume of boxes, spheres, cylinders, and cones.

Weighted Average calculates weighted average from any number of values and weights, with support for percentage weights and grade calculations.

A grading method where different assignments or categories contribute different percentages to the final grade. Accounts for the relative importance of each assessment.

Z-Score calculates z-scores and percentile rankings for data points.

Run one-sample, two-sample, or one-proportion z-tests from summary statistics, with z-statistics, p-values, confidence intervals, and significance guidance.

3D Distance calculates distance between two points in 3D space using the distance formula, plus the midpoint and the vector between them.