Math & Statistics calculators
Percentages, fractions, algebra, statistics, probability and number tools.
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Average CalculatorFind the mean of any list of numbers, plus median, mode and rangeCombination CalculatorCount how many ways to choose r items from n, order not matteringCompleting the Square CalculatorRewrite ax² + bx + c in vertex form a(x − h)² + k, step by stepConfidence Interval CalculatorGet the confidence interval for a mean or a proportion in one stepCross Product CalculatorFind a × b for two 3D vectors, with magnitude, angle and stepsDecimal to Fraction CalculatorTurn any decimal — even a repeating one — into a simplified fractionDefinite Integral CalculatorIntegrate any function between two limits and see the area under the curveDerivative CalculatorDifferentiate any function and get the slope and tangent line at a pointDeterminant CalculatorFind the determinant of any square matrix up to 6×6, with stepsDomain and Range CalculatorFind the domain and range of common functions in interval notationEigenvalue & Eigenvector CalculatorGet eigenvalues, eigenvectors and the characteristic polynomialExponent CalculatorRaise any number to any power — negative, decimal or fractionalFactoring Polynomials CalculatorFactor polynomials completely over the integers, with the method shownFraction CalculatorAdd, subtract, multiply and divide fractions with simplified stepsFraction to Decimal CalculatorConvert any fraction or mixed number to a decimal and spot the repeatGCF CalculatorFind the greatest common factor of two or more numbers, with stepsGraphing CalculatorPlot one or two functions and find roots, intersections and valuesInequality SolverSolve linear, quadratic and compound inequalities in interval notationLCM CalculatorFind the least common multiple of any set of numbers, with stepsLimit CalculatorEvaluate limits at a point or at infinity, including one-sided limitsLinear Equation SolverSolve one-variable linear equations with brackets and fractions, step by stepLinear Interpolation CalculatorFind the value between (or beyond) two known points on a straight lineLogarithm CalculatorFind log base 10, natural log, log base 2, any base, or the antilogLong Division CalculatorDivide step by step and get the quotient, remainder and decimalMatrix CalculatorAdd, multiply, invert and transpose matrices, and find determinantsMatrix Inverse CalculatorInvert a square matrix up to 6×6 with exact fractions and every row stepMean, Median, Mode CalculatorPaste a list of numbers to get the mean, median, mode and rangeMultiplication Table GeneratorMake any times table chart, a single table list, or a printable quizOrder of Operations CalculatorEvaluate any expression with PEMDAS/BODMAS and see every stepP-Value CalculatorTurn a z, t, chi-square or F statistic into a precise p-valuePartial Derivative CalculatorDifferentiate f(x, y, z) with respect to any variable and evaluate itPercentage CalculatorSolve any percentage question: X% of Y, what percent, % change and morePercentage Change CalculatorSee the percent increase or decrease between an old and a new valuePrime Factorization CalculatorBreak any number into prime factors, with exponents and ladder stepsProbability CalculatorCombine two events: both, either, neither, and over repeated trialsQuadratic Equation SolverSolve ax² + bx + c = 0 for real or complex roots, with vertex and graphRatio CalculatorSimplify a ratio, scale it up or down, or solve A:B = C:D for the missing termRiemann Sum CalculatorApproximate an integral with left, right, midpoint or trapezoid sumsRoman Numeral ConverterTurn numbers into Roman numerals and decode Roman numerals instantlyRREF CalculatorReduce any matrix to reduced row echelon form with exact fractionsSample Size CalculatorFind how many survey responses you need for your margin of errorScientific CalculatorFree online scientific calculator with trig, logs, powers and rootsScientific Notation CalculatorConvert to and from scientific, E and engineering notation, and do mathSignificant Figures CalculatorCount sig figs and round any number to the significant figures you needSquare Root CalculatorFind any square root as a decimal and in simplest radical formStandard Deviation CalculatorSample and population standard deviation, variance and mean in one stepSystem of Equations SolverSolve 2×2 and 3×3 linear systems with Cramer’s rule, step by stepTangent Line CalculatorFind the tangent and normal line equations of a curve at any pointTaylor Series CalculatorExpand any function as a Taylor or Maclaurin polynomial around a pointVertex Form CalculatorConvert a parabola between standard and vertex form and find its vertexWeighted Average CalculatorAverage values that count differently — grades, prices, portfoliosZ-Score CalculatorTurn a raw score into a z-score, percentile and probability
More math & statistics tools
Absolute Value Equation SolverSolve |ax + b| = c and absolute value inequalities, both cases shownAntilog CalculatorFind the antilogarithm (inverse log) of a number in any baseArea Between Curves CalculatorFind the area enclosed between two curves, with intersections found for youArithmetic Sequence CalculatorFind the nth term and the sum of any arithmetic sequenceAsymptote CalculatorFind vertical, horizontal and slant asymptotes and holes of a rational functionAverage Rate of Change CalculatorFind the slope of the secant line of any function over an intervalBinary CalculatorAdd, subtract, multiply, divide and AND/OR/XOR binary numbers instantlyBinomial Distribution CalculatorFind exact, at-most and at-least probabilities for n independent trialsBinomial Expansion CalculatorExpand (ax + by)ⁿ term by term and find any specific termChi-Square CalculatorRun a chi-square goodness-of-fit or independence test with p-valueComparing Fractions CalculatorCompare and order fractions from least to greatest with a common denominatorCorrelation Coefficient CalculatorMeasure how strongly two variables move together with Pearson’s rCramer's Rule CalculatorSolve 2×2 and 3×3 linear systems using determinants, step by stepCritical Points CalculatorFind critical points, local maxima and minima of any function on an intervalCube Root and Nth Root CalculatorFind the cube root, or any nth root, of a number with simplified formDifferential Equation SolverSolve first- and second-order ODEs numerically with Euler or Runge–KuttaDivisibility Rules CheckerTest any whole number for divisibility by 2–12 and see which rule appliesExponential Equation SolverSolve a·bˣ = c and similar exponential equations with logarithms, step by stepExponential Growth and Decay CalculatorProject exponential growth or decay and find doubling time or half-lifeFactor CalculatorList every factor and factor pair of a whole number instantlyFactorial CalculatorCompute n! exactly — every digit — even for very large nGeometric Sequence CalculatorFind the nth term, partial sum and infinite sum of a geometric sequenceInterquartile Range CalculatorFind Q1, Q3, the IQR, outlier fences and the five-number summaryInverse Function CalculatorFind f⁻¹(x) algebraically and check it by composing f(f⁻¹(x)) = xLaplace Transform CalculatorFind the Laplace transform of f(t) or the inverse Laplace transform of F(s)Linear Regression CalculatorFit a least-squares line of best fit and predict new y valuesMargin of Error CalculatorFind the ± margin of error for any survey, poll or sample proportionMixed Number CalculatorAdd, subtract, multiply and divide mixed numbers with simplified answersModular Inverse CalculatorFind a⁻¹ mod m with the extended Euclidean algorithm, step by stepModulo CalculatorCompute a mod n and the remainder, with negative and decimal numbersNormal Distribution CalculatorFind probabilities and cut-off values under any normal (bell) curveNth Root CalculatorFind any root of a number, simplify the radical and list all complex rootsPartial Fraction Decomposition CalculatorBreak a rational function into simple fractions with exact coefficientsPascal's Triangle GeneratorBuild Pascal’s triangle to any row and read off binomial coefficientsPercent Error CalculatorCompare a measured value with the true value to get percent errorPercent to Fraction ConverterTurn a percentage into a simplified fraction and decimal — or back againPercentage Difference CalculatorFind the percent difference between two values when neither is the baselinePercentile CalculatorFind the value at any percentile, or the percentile rank of a scorePermutation CalculatorCount ordered arrangements nPr, with or without repetitionPolar Graphing CalculatorPlot polar r(θ) and parametric curves, with area and arc lengthPolynomial Long Division CalculatorDivide any two polynomials with every long-division step shownPolynomial Roots CalculatorFind every real and complex root of a polynomial, with multiplicitiesPrime Number CheckerCheck if a number is prime, factor it, and list primes in any rangePrime Number GeneratorList every prime in a range, or the first n primes, with a fast sieveProportion CalculatorSolve a/b = c/d for the missing value with cross multiplicationRepeating Decimal to Fraction CalculatorConvert recurring decimals like 0.(36) or 0.1666… into exact fractionsReverse Percentage CalculatorWork back to the original number before a percentage was added or removedRounding CalculatorRound any number to decimals, whole numbers, tens, hundreds or thousandsSimplify Fractions CalculatorReduce any fraction to lowest terms and see the GCF stepsSimplify Radicals CalculatorPut square roots and cube roots in simplest radical form, step by stepT-Test CalculatorOne-sample, paired and two-sample t-tests with p-value and confidence intervalTrapezoidal & Simpson's Rule CalculatorApproximate a definite integral three ways and compare the errorsVector Projection CalculatorProject vector a onto b: scalar and vector projections, plus the rejectionVolume of Revolution CalculatorVolume of a solid of revolution by the disk, washer or shell methodANOVA CalculatorOne-way ANOVA table with F statistic, p-value and effect sizeBig Number CalculatorExact arithmetic on huge integers and long decimals — no rounding errorsCoefficient of Variation CalculatorMeasure relative variability (CV %) of any data set in one stepCollatz Sequence CalculatorFollow the 3n + 1 sequence from any number down to 1Complex Number CalculatorAdd, multiply, divide and convert complex numbers to polar formCubic Equation SolverFind all three roots of ax³ + bx² + cx + d = 0, real and complexCurve Arc Length CalculatorFind the length of any curve y = f(x) between two x valuesDice Probability CalculatorOdds of rolling any total with any number of dice — d4 to d100Digit Sum CalculatorAdd up the digits of any number and find its digital root instantlyEmpirical Rule CalculatorApply the 68-95-99.7 rule to any mean and standard deviationEngineering Notation ConverterConvert any number to engineering notation and the matching SI prefixEuler's Totient CalculatorCount the integers up to n that are coprime to n, with the workingExpanded Form CalculatorBreak any number into place values and write it in wordsExpected Value CalculatorFind the long-run average, variance and fair price of any outcome tableFibonacci CalculatorGet the exact nth Fibonacci number and the sequence up to itFourier Series CalculatorFind Fourier coefficients and plot partial sums of a periodic functionFunction Composition CalculatorCompose two functions both ways and evaluate the result at any xGolden Ratio CalculatorSplit any length by φ ≈ 1.618 or find the matching golden segmentGram-Schmidt CalculatorTurn a set of vectors into an orthonormal basis, with exact fractionsImplicit Differentiation CalculatorFind dy/dx for any equation in x and y, plus the slope at a pointInflection Point CalculatorLocate inflection points and where a curve is concave up or downLong Multiplication CalculatorMultiply multi-digit numbers and see every step of the workingLU Decomposition CalculatorFactor a square matrix into lower and upper triangular matricesMatrix Rank CalculatorFind the rank and nullity of any matrix with exact row-reduction stepsModular Exponentiation CalculatorCompute a^b mod n instantly for huge numbers, with square-and-multiply stepsNewton's Method CalculatorFind a root of any equation with Newton–Raphson, every iteration shownNull Space CalculatorGet a basis for the kernel, column space and row space of any matrixOdds to Probability CalculatorConvert odds for or against into a probability percentage — and backOutlier CalculatorFind outliers in a data set with the 1.5 × IQR fence testPoisson Distribution CalculatorProbability of exactly, at most or at least k events at an average rate λRationalize the Denominator CalculatorRemove square roots from a denominator using conjugates, step by stepRecursive Sequence CalculatorGenerate the terms of any recurrence relation, with sums, ratios and a graphSeries Convergence CalculatorTest an infinite series for convergence and see its partial sumsSummation (Sigma) CalculatorEvaluate Σ sigma-notation sums of any expression over a range of nSynthetic Division CalculatorDivide a polynomial by (x − c) and see every step of the tableauVector CalculatorDot product, cross product, magnitude and angle for 2D and 3D vectors