Math Tools
Fraction, ratio, average, standard deviation, prime, GCD/LCM, quadratic, permutation, Roman numeral, triangle and base-conversion calculators — instant, accurate and free.
98 free tools
Fraction Calculator
Add, subtract, multiply and divide two fractions online. Get the result as an improper fraction, a simplified fraction, a mixed number and a decimal.
Fraction Simplifier
Reduce any fraction to its lowest terms online. See the greatest common divisor used, the simplified fraction, the mixed number and the decimal value.
Decimal to Fraction Converter
Convert a decimal to a fraction online. Handles terminating and repeating decimals, and returns the exact fraction, simplified form and mixed number.
Ratio Calculator
Simplify a ratio to its lowest terms or solve a proportion A:B = C:? to find the missing value. Free online ratio calculator with clear working.
Average Calculator
Calculate the mean, median, mode, range, sum, count, minimum and maximum of a list of numbers. Free online average calculator with instant results.
Standard Deviation Calculator
Calculate population and sample standard deviation and variance from a list of numbers. Free online tool showing the mean, count and formula steps.
Prime Number Checker
Check whether a number is prime or composite. See the smallest factor and the full list of factors for any integer up to billions, instantly and privately.
Prime Factorization Calculator
Find the prime factorization of any integer. See the prime factors with exponents and the product form like 2² × 3 × 5, calculated instantly in your browser.
GCD & LCM Calculator
Find the greatest common divisor (GCD) and least common multiple (LCM) of two or more integers using Euclid's algorithm, with the working shown.
Quadratic Equation Solver
Solve any quadratic equation ax² + bx + c = 0. Get real or complex roots, the discriminant, vertex and axis of symmetry with clear step-by-step working.
Permutation & Combination Calculator
Calculate permutations (nPr) and combinations (nCr) instantly from n and r, with the factorial formulas shown. Free online nPr and nCr calculator.
Roman Numeral Converter
Convert numbers to Roman numerals and Roman numerals back to numbers (1–3999). Free two-way Roman numeral converter with input validation.
Number to Words Converter
Convert numbers to words in English, including decimals, negatives and a currency mode for dollars and cents. Free online number-to-words spelling tool.
Factorial Calculator
Calculate the factorial of any number (n!) exactly using BigInt, and see the full result plus its digit count. Free online factorial calculator.
Percentage to Fraction Converter
Convert between percentages, fractions and decimals instantly, with the fraction fully simplified. Free online percent to fraction and decimal converter.
Triangle Solver
Solve any triangle from known sides and angles (SSS, SAS, ASA, AAS, SSA) using the laws of sines and cosines. Get all sides, angles, area and perimeter.
Pythagorean Theorem Calculator
Solve the Pythagorean theorem: enter any two sides of a right triangle to find the third, plus the area. Free a² + b² = c² calculator with steps.
Slope Calculator
Find the slope, midpoint, distance, line equation and angle of incline from two points. Free slope calculator that handles vertical lines too.
Number Base Converter
Convert whole numbers between any bases from 2 to 36, with from-base and to-base selectors and digit validation. Free online number base converter.
Rounding Calculator
Round any number to decimal places, significant figures or the nearest multiple, with round, floor and ceiling modes. Free online rounding calculator.
Percentage Change Calculator
Work out the percentage increase or decrease between an old and a new value. See the absolute change and whether it went up or down, instantly and privately.
Exponent Calculator
Calculate base raised to any exponent online, including negative and fractional powers. See the result and the full expression, computed instantly in your browser.
Square Root Calculator
Find the square root or any nth root of a number online. Get the decimal value and the simplified radical form where it comes out clean, all in your browser.
Logarithm Calculator
Calculate the logarithm of a number with any base, including log base 10, natural log (ln) and log base 2. See the result and an inverse check, all in your browser.
Modulo Calculator
Calculate a mod n and the quotient online, with correct handling of negative numbers. See both the truncated remainder and the floored mathematical modulo.
Arithmetic Sequence Calculator
Find the nth term and the sum of an arithmetic sequence from the first term, common difference and n. See the formula and the first several terms listed out.
Geometric Sequence Calculator
Find the nth term and sum of a geometric sequence from the first term, common ratio and n. Includes the infinite sum when the ratio is between −1 and 1.
Fibonacci Calculator
Find the nth Fibonacci number and list the sequence up to n. Uses BigInt for exact results, so even very large Fibonacci numbers stay precise in your browser.
Prime Number Generator
Generate all prime numbers up to a limit, or the first N primes, using a fast sieve. See the full list and the total count, computed instantly in your browser.
Circle Calculator
Enter any one of radius, diameter, circumference or area and calculate the other three using π. Fast, accurate circle geometry, all in your browser.
Scientific Notation Converter
Convert numbers to and from scientific notation (a × 10^b). Handles very large and very small values and shows E-notation too, all computed in your browser.
Mean, Median & Mode Calculator
Calculate the mean, median, mode, range, sum and count from a list of numbers. Handles no-mode and multi-modal data, all computed privately in your browser.
Binary Search Calculator
Visualize binary search on a sorted list. Count worst-case comparisons for any array size and trace each step — low, high, mid and decision — in your browser.
System of Equations Solver
Solve systems of 2, 3 or 4 linear equations by Gauss-Jordan elimination. See every step, and get clear answers for unique, none or infinite solutions.
Matrix Calculator
Add, subtract and multiply matrices up to 6×6, transpose them or scale by a number. Type matrices as simple rows and get instant, copyable results.
Determinant Calculator
Compute the determinant of any square matrix up to 6×6 instantly. See the full cofactor expansion for 2×2 and 3×3 matrices, worked step by step.
Matrix Inverse Calculator
Invert any square matrix up to 6×6 using Gauss-Jordan elimination on [A|I]. Detects singular matrices and verifies the result with A × A⁻¹ = I.
Cubic Equation Solver
Solve ax³ + bx² + cx + d = 0 and get all three roots, real or complex, using Cardano's method with a discriminant classification and high accuracy.
Polynomial Roots Calculator
Find every real and complex root of a polynomial from its coefficients using the Durand–Kerner method. Works for any degree from 1 to 10, instantly.
Synthetic Division Calculator
Divide a polynomial by (x − r) using synthetic division. See the classic three-row tableau, the quotient coefficients and the remainder, step by step.
Linear Equation Solver
Solve linear equations like 3x + 5 = 2x − 7 instantly. Type the equation or enter coefficients, and follow the worked steps to the value of x.
Discriminant Calculator
Compute the discriminant b² − 4ac of a quadratic equation, classify its roots as two real, one repeated or complex, and see the actual root values.
Completing the Square Calculator
Convert ax² + bx + c into vertex form a(x − h)² + k with every intermediate step shown. Get the vertex coordinates and check your algebra homework fast.
Parabola Calculator
Analyze any parabola from standard or vertex form: vertex, focus, directrix, axis of symmetry, intercepts and latus rectum — with a live graph.
Slope Intercept Form Calculator
Find the equation of a line from two points or from a slope and a point. Get y = mx + b, point-slope and standard form, plus a drawn line graph.
Online Graphing Calculator
Plot up to three y = f(x) functions on one graph. Supports sin, cos, tan, log, sqrt, powers and more, with adjustable window and PNG export.
Variance Calculator
Calculate population and sample variance from a list of numbers. See the mean, squared deviation table and standard deviation, computed in your browser.
Z Score Calculator
Convert a raw value to a z-score with z = (x − μ)/σ, or turn a z-score back into a value. Includes left, right and between probabilities from the normal curve.
Percentile Calculator
Find the value at any percentile of a data set using nearest-rank and linear-interpolation methods, or find what percentile a given value falls at.
Quartile Calculator (Q1, Q3, IQR)
Get the five-number summary of any data set: min, Q1, median, Q3 and max, plus the interquartile range and 1.5×IQR outlier fences with flagged outliers.
Weighted Average Calculator
Compute a weighted average from value and weight pairs: Σ(value × weight) ÷ Σ(weights). Add rows for grades, portfolios or ratings and see each weight's share.
Correlation Coefficient Calculator
Calculate Pearson's correlation coefficient r and r² for paired x, y data. Get a plain-English read of the strength and direction of the linear relationship.
Linear Regression Calculator
Fit y = mx + b to paired data by ordinary least squares. Get slope, intercept, r², residuals and a scatter plot with the best-fit line drawn on canvas.
Probability Calculator
Work out probabilities for one or two events: complement, union, intersection, conditional probability and the chance of at least one success in n trials.
Normal Distribution Calculator
Compute normal distribution probabilities for any mean and standard deviation: P(X<x), P(X>x), P(a<X<b), the PDF, plus an inverse quantile mode.
Binomial Distribution Calculator
Compute binomial probabilities P(X=k), P(X≤k) and P(X≥k) for n trials with success chance p, plus the distribution's mean, variance and standard deviation.
Confidence Interval Calculator
Build a confidence interval for a mean (z or t) or a proportion. Get the margin of error, lower and upper bounds, and the critical value used, step by step.
Sample Size Calculator
Find how many responses your survey or study needs: n = z²p(1−p)/e², with finite population correction, for any confidence level and margin of error.
Margin of Error Calculator
Calculate the margin of error for a survey or sample: z × √(p(1−p)/n) for proportions or z × σ/√n for means, with finite population correction.
Fraction to Decimal Converter
Convert any fraction to its exact decimal form, including repeating decimals like 1/7 = 0.(142857). See the repeating block and period instantly.
Mixed Number Calculator
Add, subtract, multiply and divide mixed numbers online. Converts to improper fractions, simplifies with the GCD, and shows the working step by step.
Proportion Calculator
Solve proportions online: enter three values of a/b = c/d and the calculator finds the missing one by cross-multiplication, or checks if two ratios are proportional.
Significant Figures Calculator
Count the significant figures in any number and round values to a chosen number of sig figs, with the counting rules explained for each answer.
Cube Root Calculator
Find the cube root of any number, including negatives, detect perfect cubes, and compute any nth root online with instant, private results.
Factors Calculator
List every factor of a number with factor pairs, count and sum. Flags primes and perfect, abundant or deficient numbers instantly in your browser.
Long Division Calculator
Do long division with every step shown: the classic bring-down layout, partial products, remainder and optional decimal places, rendered instantly.
Big Number Calculator
Add, subtract, multiply, divide and raise huge integers to powers with exact arbitrary-precision arithmetic — hundreds or thousands of digits, no rounding.
Trigonometry Calculator
Evaluate sin, cos, tan, csc, sec and cot in degrees or radians, with exact special-angle values, reference angles, quadrants and all six inverse functions.
Unit Circle Calculator
See any angle drawn on the unit circle with its (cos θ, sin θ) point, radians in π form, quadrant and reference angle — updated live as you type.
Vector Calculator
Add, subtract and scale 2D or 3D vectors, compute dot and cross products, magnitudes, unit vectors and the angle between vectors instantly online.
Complex Number Calculator
Add, subtract, multiply, divide and raise complex numbers to powers. Converts between rectangular a+bi and polar form with modulus, argument and conjugate.
Truth Table Generator
Generate the complete truth table for any boolean expression with AND, OR, NOT, XOR, implies and iff — up to 6 variables, with tautology detection.
Eigenvalue and Eigenvector Calculator
Find eigenvalues and eigenvectors of 2×2 and 3×3 matrices from the characteristic polynomial, with algebraic and geometric multiplicity spelled out.
Characteristic Polynomial Calculator
Compute det(λI − A) for matrices up to 6×6 with the Faddeev-LeVerrier recursion, plus trace and determinant cross-checks and a Cayley-Hamilton proof.
RREF Calculator
Reduce any matrix to reduced row echelon form with every row operation listed, pivot columns marked, and the rank and consistency of the system reported.
Matrix Rank Calculator
Find the rank of any matrix by exact row reduction, then get the nullity from the rank-nullity theorem plus full row rank, column rank and singularity.
Null Space (Kernel) Calculator
Solve A·x = 0 to get a basis for the null space, its dimension, and the general solution in parametric vector form — all in exact fractions.
Linear Independence Calculator
Test whether a set of vectors is linearly independent by comparing rank to vector count, and see the explicit relation when they turn out to be dependent.
LU Decomposition Calculator
Factor a square matrix into P, L and U by Doolittle elimination with partial pivoting, then use the factorisation to get the determinant and solve A·x = b.
QR Decomposition Calculator
Factor a matrix into an orthogonal Q and upper-triangular R using Householder reflections, with an orthogonality check and least-squares solving.
Gram-Schmidt Calculator
Turn any set of vectors into an orthogonal or orthonormal basis with the modified Gram-Schmidt process, showing every projection subtraction as a step.
Cramer's Rule Calculator
Solve linear systems with Cramer's rule as a ratio of determinants, seeing each replaced matrix, its cofactor expansion and the exact fractional answer.
Matrix Power Calculator
Raise a square matrix to any whole power using binary exponentiation, with the intermediate squarings shown and negative powers via the exact inverse.
Adjugate Matrix Calculator
Build the cofactor matrix from minors, transpose it into the adjugate, and see both A·adj(A) = det(A)·I and A⁻¹ = adj(A)/det(A) verified entry by entry.
Vector Projection Calculator
Project one vector onto another to get the vector projection, scalar projection, orthogonal rejection and the angle between, for 2D or 3D vectors.
P-Value Calculator
Turn a z, t, chi-square or F test statistic into left-tail, right-tail and two-tailed p-values, with the critical value and a reject or fail-to-reject verdict.
T-Test Calculator
Run a one-sample, paired or two-sample t-test from raw data. Get t, degrees of freedom, exact p-values, the critical value, Cohen's d and a confidence interval.
Chi-Square Test Calculator
Run a chi-square goodness-of-fit test or a test of independence on a contingency table. Get the statistic, degrees of freedom, exact p-value and Cramér's V.
One-Way ANOVA Calculator
Build a complete one-way ANOVA table from pasted groups: sums of squares, degrees of freedom, mean squares, the F statistic, an exact p-value and eta squared.
Poisson Distribution Calculator
Calculate Poisson probabilities for a given rate: P(X = k), cumulative tails, range probabilities, mean and variance, with a bar chart and full probability table.
Geometric Distribution Calculator
Work out geometric probabilities using either convention: trials until the first success or failures before it. Includes CDF, mean, variance and a bar chart.
Hypergeometric Distribution Calculator
Calculate probabilities for sampling without replacement: P(X = k), cumulative tails, mean and variance with the finite population correction, plus a chart.
Exponential Distribution Calculator
Calculate exponential distribution probabilities from a rate or a mean: PDF, CDF, survival, interval probability, median, variance and the inverse quantile.
Bayes' Theorem Calculator
Apply Bayes' theorem to get a posterior probability, or switch to diagnostic-test mode for positive and negative predictive value with an expanded 2 × 2 table.
Expected Value Calculator
Calculate the expected value, variance and standard deviation of a discrete random variable, or switch to wager mode for the EV per unit staked and the house edge.
Covariance Calculator
Calculate sample and population covariance from paired data, with the full deviation-product table, both means and Pearson's correlation coefficient alongside.
Dice Probability Calculator
Get exact probabilities for the sum of any number of dice with any number of sides, plus 'at least one' odds, a histogram and the full ways-to-roll table.
Frequency Distribution Calculator
Group raw data into classes using Sturges' rule, the square-root rule or a width you choose, then get frequencies, cumulative columns, grouped stats and a histogram.