Math Calculators
Arithmetic, algebra, geometry, statistics, probability and number theory.
258 of 258 available now
General Math
Scientific CalculatorA full scientific calculator with trigonometry, logarithms, memory and history.Basic CalculatorA clean four-function calculator with percentage and memory keys.Percentage CalculatorSolve every common percentage question: of, increase, decrease and difference.Percent Error CalculatorCompare a measured value against the true value as a percent error.Fraction CalculatorAdd, subtract, multiply and divide fractions with simplified results and steps.Average CalculatorCompute the mean of any list of numbers, plus sum, count and range.Rounding CalculatorRound to decimals, significant figures or the nearest multiple, with every rounding mode.Long Division CalculatorDivide with a full worked long-division layout, quotient and remainder.Big Number CalculatorExact arbitrary-precision arithmetic on numbers far beyond floating point limits.Modulo CalculatorCompute the remainder of a division, with true mathematical modulo for negatives.Scientific Notation CalculatorConvert to and from scientific, engineering and E notation, and do arithmetic in it.Percentage Increase CalculatorCalculate the percentage increase between two values with the absolute change shown.Percentage Decrease CalculatorCalculate the percentage decrease between two values with the absolute drop shown.Percentage Difference CalculatorFind the percentage difference between two values relative to their average.Reverse Percentage CalculatorFind the original number before a percentage increase or decrease was applied.Fraction Comparison CalculatorCompare two fractions and determine which is larger, smaller, or if they are equal.Decimal to Fraction CalculatorConvert any decimal number to a fully reduced fraction using integer arithmetic.Mixed Fraction CalculatorConvert between improper fractions and mixed numbers in both directions.Percentage to Fraction CalculatorConvert a percentage value to a fully simplified fraction.Long Multiplication CalculatorMultiply two numbers with a full column-by-column working showing every partial product.Long Subtraction CalculatorSubtract two numbers column-by-column with borrowing steps shown.Weighted Average CalculatorCompute the weighted mean of values with individual weights or frequencies.Harmonic Mean CalculatorCalculate the harmonic mean of a set of positive numbers, ideal for rates and ratios.Geometric Mean CalculatorCalculate the geometric mean of positive numbers, ideal for growth rates and ratios.Absolute Value CalculatorFind the absolute value (magnitude) of any real number and its distance from zero.Reciprocal CalculatorFind the reciprocal (multiplicative inverse) of a number or fraction.Cube (x³) CalculatorRaise any number to the third power and see the intermediate squaring step.
Algebra
Exponent CalculatorRaise any base to any power, including negative and fractional exponents.Root CalculatorFind square roots, cube roots and any nth root of a number.Logarithm CalculatorCompute logarithms in any base, plus natural log and antilog.Quadratic Formula CalculatorSolve any quadratic equation with real or complex roots, vertex and discriminant.Slope CalculatorFind the slope, angle and line equation through two points.Matrix CalculatorAdd, multiply, transpose and invert matrices, and find determinants.Ratio CalculatorSimplify ratios, solve proportions and scale ratios up or down.Number Sequence CalculatorFind terms and sums of arithmetic, geometric and Fibonacci sequences.Half-Life CalculatorSolve exponential decay for half-life, mean lifetime, decay constant or remaining quantity.Trigonometry CalculatorEvaluate all six trig functions and their inverses in degrees or radians.Linear Equation SolverSolve ax + b = 0 for x, showing the solution and verification step.Simultaneous Equation SolverSolve a system of two linear equations in two unknowns using Cramer's rule.Cubic Equation SolverFind all three roots of ax³+bx²+cx+d=0 using the depressed-cubic method, including complex roots.Quartic Equation SolverSolve ax⁴+bx³+cx²+dx+e=0 for all four roots via Ferrari's resolvent-cubic method.Polynomial SolverFind rational roots of a polynomial up to degree 6 using the rational root theorem.Polynomial DivisionDivide one polynomial by another using synthetic or long division, showing quotient and remainder.Polynomial ExpansionExpand (ax+b)^n using the binomial theorem, showing each term and coefficient.Polynomial FactorizationFactor a polynomial into linear factors over the rationals using the rational root theorem.Polynomial RootsFind all real and complex roots of a polynomial up to degree 4 using exact algebraic methods.FOIL CalculatorMultiply two binomials (ax+b)(cx+d) using the FOIL method with step-by-step breakdown.Completing the SquareRewrite ax²+bx+c into vertex form a(x−h)²+k and identify the vertex coordinates.Rational Expression SimplifierAdd, subtract, multiply or divide two rational expressions (fractions of polynomials).Radical SimplifierSimplify √n by extracting the largest perfect-square factor: √n = a√b.Function CalculatorEvaluate a mathematical function f(x) at a given value using the built-in expression parser.Composite Function CalculatorCompute (f∘g)(x) = f(g(x)) by evaluating two functions in sequence at a given x value.Inverse Function CalculatorNumerically approximate f⁻¹(y) by finding x where f(x)=y using bisection search.Domain CalculatorEstimate the domain of f(x) by sampling the expression parser across a wide range of x values.Range CalculatorEstimate the range of f(x) by evaluating it across its domain and reporting observed min/max.Piecewise Function CalculatorEvaluate a piecewise-defined function at x by selecting the matching interval branch.Function OperationsCompute (f+g)(x), (f−g)(x), (f·g)(x) and (f/g)(x) for two expressions at a given x.
Linear Algebra
Matrix Addition CalculatorAdd two matrices element-wise with dimension validation and step-by-step output.Matrix Multiplication CalculatorMultiply two matrices of compatible dimensions with full row-by-column working.Matrix Inverse CalculatorCompute the inverse of a square matrix via LU decomposition with singularity detection.Matrix Rank CalculatorDetermine the rank of a matrix by row-reducing to echelon form.Matrix Determinant CalculatorCompute the determinant of any square matrix using LU factorisation with partial pivoting.Matrix Eigenvalues CalculatorFind eigenvalues via the characteristic polynomial (2×2, 3×3) or QR iteration (larger symmetric).Matrix Eigenvectors CalculatorCompute eigenvectors for each eigenvalue of a 2×2 or 3×3 real matrix.Gaussian Elimination CalculatorRow-reduce any matrix to echelon and reduced row-echelon form with pivot tracking.LU Decomposition CalculatorFactor a square matrix into lower and upper triangular matrices with partial pivoting.QR Decomposition CalculatorDecompose a matrix into an orthogonal Q and upper-triangular R via Gram-Schmidt.Cholesky Decomposition CalculatorFactor a symmetric positive-definite matrix into L·Lᵀ with definiteness verification.Vector Addition CalculatorAdd two or more vectors component-wise in any dimension and show the resultant.Dot Product CalculatorCompute the dot (inner) product of two vectors with geometric interpretation.Cross Product CalculatorFind the cross product of two 3D vectors with magnitude and direction.Vector Projection CalculatorProject one vector onto another and compute the scalar and vector projections.Vector Angle CalculatorCalculate the angle between two vectors using the dot product formula.Norm CalculatorCompute L1, L2 (Euclidean), and L-infinity norms of a vector.Projection Matrix CalculatorBuild the orthogonal projection matrix onto the column space of a given matrix.Linear Transformation CalculatorApply a matrix transformation to a vector and visualise the mapped coordinates.
Geometry
Triangle CalculatorSolve any triangle from three known values using the sine and cosine rules.Right Triangle CalculatorSolve a right triangle from any two values, with angles, area and perimeter.Pythagorean Theorem CalculatorFind any missing side of a right triangle using a² + b² = c².Circle CalculatorSolve a circle from radius, diameter, circumference or area — any one gives the rest.Area CalculatorCalculate the area of rectangles, triangles, circles, trapezoids, ellipses and sectors.Volume CalculatorFind the volume of spheres, cones, cubes, cylinders, pyramids and more.Surface Area CalculatorCompute the surface area of common three-dimensional solids.Distance CalculatorMeasure distance between 2D or 3D points, and great-circle distance between coordinates.Triangle Area CalculatorCalculate the area of a triangle from its base and height.Triangle Perimeter CalculatorFind the perimeter of a triangle by summing all three side lengths.Heron's Formula CalculatorCompute triangle area from three sides using Heron's formula with triangle inequality validation.Isosceles Triangle CalculatorCalculate area, perimeter, height and angles of an isosceles triangle from its equal sides and base.Equilateral Triangle CalculatorCompute all properties of an equilateral triangle from one side length.Scalene Triangle CalculatorCalculate area, perimeter and angles of a scalene triangle from three unequal sides.Chord Length CalculatorCalculate the length of a chord from the circle radius and central angle.Arc Length CalculatorCompute the arc length of a circle given its radius and central angle in degrees.Sector Area CalculatorFind the area of a circular sector from its radius and central angle.Segment Area CalculatorCalculate the area of a circular segment (sector minus triangle) from radius and angle.Annulus Area CalculatorCompute the area of an annulus (ring) from the outer and inner radii.Ellipse CalculatorCalculate area, circumference, eccentricity and foci of an ellipse from its semi-axes.Parabola CalculatorFind the vertex, focus, directrix and axis of symmetry of a parabola y=ax²+bx+c.Hyperbola CalculatorCompute eccentricity, foci, vertices and asymptotes of a hyperbola from a and b.Rectangle CalculatorCalculate area, perimeter and diagonal of a rectangle from length and width.Square CalculatorCompute area, perimeter, diagonal and inradius of a square from its side length.Rhombus CalculatorCalculate area, perimeter and angles of a rhombus from its side and diagonals.Kite CalculatorFind the area and perimeter of a kite from its two diagonals and side pairs.Trapezoid CalculatorCalculate area, perimeter and median of a trapezoid from its parallel sides and height.Pentagon CalculatorCompute area, perimeter, apothem and interior angle of a regular pentagon.Hexagon CalculatorCompute area, perimeter, apothem and interior angle of a regular hexagon.Regular Polygon CalculatorCalculate area, perimeter, apothem and angles of any regular polygon given sides and length.Sphere CalculatorCalculate volume, surface area, diameter and circumference of a sphere from its radius.Cube (Solid) CalculatorCompute volume, surface area, face diagonal and space diagonal of a cube.Cuboid CalculatorCalculate volume, surface area and space diagonal of a rectangular cuboid.Cylinder CalculatorCompute volume, total surface area and lateral area of a right circular cylinder.Cone CalculatorCalculate volume, total surface area, lateral area and slant height of a right cone.Pyramid CalculatorCompute volume and surface area of a regular square pyramid from base side and height.Prism CalculatorCalculate volume and surface area of a triangular prism from base dimensions and length.Torus CalculatorCompute volume and surface area of a torus from its major and minor radii.Midpoint CalculatorFind the midpoint between two points in the Cartesian plane.Line Equation CalculatorDetermine the equation of a line through two points in slope-intercept and standard forms.Angle Between Lines CalculatorCalculate the acute angle between two lines given their slopes.Point-to-Line Distance CalculatorCompute the perpendicular distance from a point to a line Ax+By+C=0.Point-Circle Position CalculatorDetermine whether a point lies inside, on, or outside a circle.Circle Equation CalculatorDerive the standard and general equations of a circle from its center and radius.Reflection CalculatorReflect a point across the x-axis, y-axis, origin, or the line y=x.Rotation CalculatorRotate a point by a given angle in degrees about an arbitrary centre of rotation.Translation CalculatorTranslate a point by a displacement vector (dx, dy) and return the image coordinates.
Trigonometry
Sin CalculatorCalculate the sine of any angle in degrees or radians with step-by-step working.Cos CalculatorCalculate the cosine of any angle in degrees or radians with step-by-step working.Tan CalculatorCalculate the tangent of any angle in degrees or radians, with pole detection.Cot CalculatorCalculate the cotangent of any angle in degrees or radians, with pole detection.Sec CalculatorCalculate the secant of any angle in degrees or radians, with pole detection.Cosec CalculatorCalculate the cosecant of any angle in degrees or radians, with pole detection.ArcSin CalculatorFind the angle whose sine equals a given value, with principal value in degrees or radians.ArcCos CalculatorFind the angle whose cosine equals a given value, with principal value in degrees or radians.ArcTan CalculatorFind the angle whose tangent equals a given value, with principal value in degrees or radians.Hyperbolic Functions CalculatorEvaluate sinh, cosh, tanh and their inverses for any real number input.SOHCAHTOA CalculatorFind a missing side or angle of a right triangle using SOH-CAH-TOA ratios.Law of Sines CalculatorSolve a triangle using the sine rule: a/sin A = b/sin B = c/sin C.Law of Cosines CalculatorSolve a triangle using the cosine rule: c² = a² + b² − 2ab·cos C.Bearing CalculatorCompute the compass bearing between two points given their coordinates.Angle of Elevation CalculatorFind the angle of elevation from horizontal distance and height above eye level.Angle of Depression CalculatorFind the angle of depression from horizontal distance and height below eye level.Triangle Trigonometry SolverSolve any triangle given three known values (SSS, SAS, ASA, AAS) using trig laws.Unit Circle CalculatorLook up exact sin, cos, tan values and coordinates for standard unit-circle angles.Trig Identity CheckerVerify a trigonometric identity numerically by sampling angles and reporting max deviation.Radian ConverterConvert an angle from degrees to radians with exact fractional-pi form when possible.Degree ConverterConvert an angle from radians to degrees with DMS (degrees-minutes-seconds) breakdown.Phase Shift CalculatorFind the phase shift of y = A·sin(Bx + C) + D and describe the full wave.Amplitude CalculatorFind the amplitude of y = A·sin(Bx + C) + D and describe the full wave properties.Period CalculatorFind the period of y = A·sin(Bx + C) + D and describe the full wave properties.
Calculus
Derivative CalculatorCompute the first derivative of polynomial, trigonometric, exponential and logarithmic terms.Second Derivative CalculatorCompute the second derivative of standard function forms to analyse concavity.Third Derivative CalculatorCompute the third derivative of standard function forms for jerk analysis.Partial Derivative CalculatorCompute partial derivatives of polynomial terms in x and y using the power rule.Gradient CalculatorCompute the gradient vector of a polynomial function in x and y at a given point.Hessian Matrix CalculatorCompute the 2×2 Hessian matrix of second partial derivatives for f(x,y) polynomials.Integral CalculatorCompute definite and indefinite integrals of polynomial, trig, exponential and log terms.Double Integral CalculatorEvaluate a double integral of a polynomial in x and y over a rectangular region.Triple Integral CalculatorEvaluate a triple integral of a monomial in x, y, z over a rectangular box region.Improper Integral CalculatorNumerically approximate improper integrals with infinite limits using adaptive truncation.Limit CalculatorEvaluate the limit of f(x) as x approaches a value by numerical approximation from both sides.L'Hôpital's Rule CalculatorApply L'Hôpital's rule numerically to evaluate 0/0 or ∞/∞ indeterminate limits.Taylor Series CalculatorCompute the Taylor series expansion of f(x) about a given point up to degree n.Maclaurin Series CalculatorCompute the Maclaurin series (Taylor expansion about 0) of f(x) up to degree n.Fourier Series CalculatorCompute Fourier cosine and sine coefficients for standard periodic waveforms.Laplace Transform CalculatorCompute the Laplace transform of standard forms: polynomials, exponentials, trig and steps.Inverse Laplace Transform CalculatorFind the time-domain function from a standard-form Laplace transform F(s).Z-Transform CalculatorCompute the Z-transform of standard discrete sequences from coefficient parameters.Inverse Z-Transform CalculatorFind the discrete sequence from a standard-form Z-transform expression.Differential Equation SolverSolve first-order ODEs numerically using RK4 given dy/dx = f(x,y) and an initial condition.Separable Equation SolverSolve separable first-order ODEs dy/dx = g(x)·h(y) numerically with RK4.
Statistics
Standard Deviation CalculatorCompute population and sample standard deviation, variance and standard error.Statistics CalculatorFull descriptive statistics for a dataset: centre, spread, quartiles, skew and outliers.Mean, Median, Mode, Range CalculatorFind all four measures of centre and spread for any list of numbers.Z-score CalculatorConvert between z-scores, raw values and normal distribution probabilities.Confidence Interval CalculatorBuild confidence intervals for a mean or proportion at any confidence level.Sample Size CalculatorDetermine the sample size needed for a target margin of error and confidence.P-value CalculatorConvert a test statistic into a p-value for z, t and chi-square tests.Variance CalculatorCalculate population or sample variance from a dataset with step-by-step squared deviations.Range Calculator (Statistics)Find the statistical range (max − min) of a dataset with extremes identified.Quartiles CalculatorCompute Q1, Q2, Q3 from a dataset using the percentile interpolation method.IQR CalculatorCalculate the interquartile range (Q3 − Q1) as a robust measure of spread.Five Number Summary CalculatorReport the minimum, Q1, median, Q3 and maximum of a dataset for box-plot construction.Outlier Detection CalculatorIdentify outliers in a dataset using Tukey's 1.5×IQR fence method.Percentile CalculatorFind the value at any percentile rank in a dataset using linear interpolation.T Score CalculatorConvert a raw score to a T score (mean 50, SD 10) given the group mean and standard deviation.Correlation CalculatorCompute Pearson's correlation coefficient r between two paired datasets.Covariance CalculatorCalculate sample or population covariance between two paired datasets.Linear Regression CalculatorFit a least-squares line y = mx + b to paired data and report slope, intercept and R².Multiple Regression CalculatorFit a multiple linear regression y = b₀ + b₁x₁ + b₂x₂ for two predictors using normal equations.ANOVA CalculatorPerform one-way ANOVA: compute SSB, SSW, F statistic and p-value for group means comparison.Chi-Square CalculatorRun a chi-square goodness-of-fit test comparing observed vs expected frequencies.T-Test CalculatorPerform a one-sample or two-sample t-test with t statistic, degrees of freedom and p-value.F-Test CalculatorCompare two sample variances with an F-test, returning the F statistic and p-value.Margin of Error CalculatorCalculate the margin of error for a survey or poll given sample size and confidence level.Probability Distribution CalculatorCalculate PMF/PDF, CDF, mean and variance for common discrete and continuous distributions.Normal Distribution CalculatorCompute PDF, CDF, and inverse CDF for the normal (Gaussian) distribution with given μ and σ.Binomial Distribution CalculatorCalculate PMF, CDF, mean and variance for the binomial distribution B(n,p).Poisson Distribution CalculatorCalculate PMF, CDF, mean and variance for the Poisson distribution with rate λ.Geometric Distribution CalculatorCalculate PMF, CDF, mean and variance for the geometric distribution (trials until first success).Uniform Distribution CalculatorCalculate PDF, CDF, mean and variance for the continuous uniform distribution on [a, b].Expected Value CalculatorCompute the expected value E[X] from a discrete probability distribution table.
Probability
Probability CalculatorCompute union, intersection, complement and conditional probabilities of events.Permutation and Combination CalculatorCount arrangements and selections with nPr, nCr, and repetition variants.Random Number GeneratorGenerate cryptographically strong random numbers in any range, with or without repeats.Conditional Probability CalculatorCalculate P(A|B) using the definition P(A∩B)/P(B) with step-by-step explanation.Probability Tree CalculatorCompute compound event probabilities for a two-stage experiment using multiplication rule.Dice Probability CalculatorCalculate the probability of rolling a target sum with a given number of fair dice.Coin Toss Probability CalculatorCalculate the probability of getting exactly k heads in n fair coin tosses.Card Probability CalculatorCalculate the probability of drawing specific cards from a standard 52-card deck.Birthday Problem CalculatorCompute the probability that at least two people in a group share a birthday.
Number Theory
Factor CalculatorList every factor of a number and identify whether it's prime.Prime Factorization CalculatorBreak any number into its prime factors with a factor tree.Greatest Common Factor CalculatorFind the GCF of several numbers using the Euclidean algorithm.Least Common Multiple CalculatorFind the LCM of several numbers, with the prime factorization behind it.Common Factor CalculatorList all factors shared by a set of numbers, not just the greatest one.Prime Number GeneratorGenerate all prime numbers up to a given limit using the Sieve of Eratosthenes.Prime CheckerTest whether a given integer is prime, with trial-division proof.Composite Number CheckerDetermine whether a number is composite and show its smallest factor.Divisibility CheckerCheck whether one integer evenly divides another and show the quotient and remainder.Factorial CalculatorCompute n! exactly using BigInt for arbitrarily large results up to 1000!.Fibonacci CalculatorCompute the nth Fibonacci number and display the sequence up to that term.Twin Prime CheckerCheck whether two numbers form a twin prime pair (both prime, difference of 2).Mersenne Prime CheckerTest whether 2ⁿ − 1 is a Mersenne prime for a given exponent n.Perfect Number CheckerDetermine whether a number equals the sum of its proper divisors.Modular Inverse CalculatorFind the modular multiplicative inverse a⁻¹ mod m using the extended Euclidean algorithm.Euler Totient CalculatorCompute Euler's totient φ(n) — the count of integers up to n that are coprime to n.Chinese Remainder Theorem CalculatorSolve a system of simultaneous congruences with pairwise coprime moduli via CRT.Euclidean Algorithm CalculatorFind the GCD of two numbers with full step-by-step Euclidean algorithm trace.Extended Euclidean Algorithm CalculatorFind GCD and Bézout coefficients x, y such that ax + by = gcd(a, b).Lucas Numbers CalculatorCompute the nth Lucas number and display the Lucas sequence up to that term.
Number Systems
Binary CalculatorDo binary arithmetic and bitwise operations, and convert between bases.Hex CalculatorHexadecimal arithmetic and conversion to binary, octal and decimal.Octal CalculatorPerform octal (base-8) arithmetic and convert between octal, decimal, binary and hex.Base ConverterConvert integers between any two bases from 2 to 36 with step-by-step working.
Discrete Math
Set Operations CalculatorCompute union, intersection, difference and symmetric difference of two sets.Venn Diagram CalculatorCalculate region counts for a two-set or three-set Venn diagram from given cardinalities.Truth Table GeneratorGenerate a complete truth table for a boolean expression with AND, OR, NOT, XOR and implies.Logic Gate CalculatorEvaluate the output of standard logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR) for given inputs.Boolean Algebra CalculatorParse and evaluate a boolean expression, enumerate all input combinations, and identify tautologies.Karnaugh Map CalculatorMinimise a boolean function of up to 4 variables using the Quine-McCluskey method.Graph Coloring CalculatorAssign colors to graph vertices using a greedy algorithm, reporting the chromatic number upper bound.Shortest Path CalculatorFind the shortest path between two vertices using Dijkstra's algorithm on a weighted edge list.Hamiltonian Path CalculatorCheck whether a Hamiltonian path exists in a small graph via backtracking search.Euler Path CalculatorDetermine whether an Euler path or circuit exists using vertex degree conditions.
Numerical Methods
Newton-Raphson CalculatorFind a root of f(x)=0 using Newton-Raphson iteration with tolerance and iteration control.Bisection Method CalculatorFind a root of f(x)=0 by bisection on a bracketing interval with convergence reporting.Secant Method CalculatorFind a root of f(x)=0 using the secant method — no derivative needed.Simpson's Rule CalculatorApproximate a definite integral using composite Simpson's 1/3 rule with n subintervals.Trapezoidal Rule CalculatorApproximate a definite integral using the composite trapezoidal rule with n subintervals.Riemann Sum CalculatorCompute left, right and midpoint Riemann sums for a function over an interval.Numerical Integration CalculatorCompare trapezoidal, Simpson's and midpoint rules side-by-side for a given integral.Euler Method CalculatorSolve an ODE numerically using Euler's forward method with step size control.Runge-Kutta CalculatorSolve an ODE numerically using the classical 4th-order Runge-Kutta method (RK4).Gauss-Jordan CalculatorSolve a system of linear equations using Gauss-Jordan elimination to reduced row-echelon form.Jacobi Method CalculatorSolve a diagonally-dominant linear system iteratively using the Jacobi method.Gauss-Seidel CalculatorSolve a diagonally-dominant linear system iteratively using the Gauss-Seidel method.Interpolation CalculatorEstimate a value between known data points using linear interpolation.Lagrange Interpolation CalculatorConstruct the Lagrange interpolating polynomial through given data points and evaluate at x.Newton Interpolation CalculatorConstruct Newton's divided-difference interpolating polynomial and evaluate at a given x.Spline Interpolation CalculatorInterpolate between data points using natural cubic splines and evaluate at a given x.