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Calculators/Maths

Maths calculators

Algebra, trigonometry, geometry and statistics, with the working shown beside every answer so you can check the method rather than trust the result.

Maths

Percentages, fractions, algebra, number theory and trigonometry, with the working shown alongside every answer rather than the result on its own.

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PercentageThe three everyday percentage questions in one place.Percentage change & differenceIncrease, decrease and the symmetric difference.Fraction arithmeticAdd, subtract, multiply or divide two fractions and simplify.Decimal ↔ fractionClosest fraction to a decimal, at a chosen precision.GCD & LCMGreatest common divisor and lowest common multiple.Quadratic equationRoots, vertex and discriminant of ax² + bx + c.Ratio & proportionSolves a : b = c : d for the missing term.Exponents & rootsPowers, nth roots and scientific notation of the result.LogarithmLog in any base, plus the natural and common logs.Scientific notationConverts between plain numbers and a × 10ⁿ.Prime check & factorisationTests primality and lists the prime factors.Permutations & combinationsOrdered and unordered selections from a set.Number base converterBinary, octal, decimal, hex and any base to 36.Roman numeral converterArabic to Roman and back, 1 to 3999.Rounding & significant figuresRound to decimals, significant figures or a nearest step.Trigonometry: solve a triangleSine and cosine rules from two sides and the included angle.Trigonometric functionssin, cos, tan and their inverses for one angle.Modulo & integer divisionQuotient, remainder and the true mathematical modulo.Random number generatorDraws numbers from a range: press recalculate for a new set.Arc LengthArc length of a circle from its radius and central angle, in degrees or radians.CuboidVolume, surface area, individual face areas and space diagonal of a cuboid from its three edge lengths.Power of 22 raised to any exponent, with a reference table of powers of 2 from 2⁰ to 2²⁰.Inverse Trigonometry (Theta)Solves backwards from a known sine, cosine or tangent ratio to the angle theta.Lowest Common Denominator CalculatorFinds the lowest common denominator of two or more fractions and rewrites each one over it.Perfect Square CalculatorChecks whether a number is a perfect square, and shows the nearest perfect squares below and above it.Fraction to Percentage CalculatorConverts a fraction to a percentage, or a percentage back to a simplified fraction.Angle of depressionThe angle below the horizontal from an elevated point down to a target, from height and horizontal distance.Percentage DecreaseNew value after a percentage decrease, or the percentage decrease between two values.Fraction to DecimalConverts a fraction to its decimal expansion, marking any repeating block clearly.Exponential FunctionEvaluates y = a × bˣ at a chosen x, with the underlying growth or decay rate.XOR CalculatorBitwise XOR of two whole numbers, with AND, OR and NOT shown alongside for comparison.Square Root CalculatorPrincipal square root of a number, whether it is a perfect square, and the nearest ones either side.Exponential GrowthProjects a value forward under a fixed percentage growth rate per period, from a starting value and number of periods.Arctan (Inverse Tangent)The angle, in degrees and radians, whose tangent equals the value you enter.Pascal's TriangleGenerates any row of Pascal's triangle as binomial coefficients, with the surrounding rows shown for context.Percentage Difference Between Two NumbersThe symmetric percentage difference between two numbers, using their average as the base, distinct from a directional percentage increase or decrease.Polar Form of a Complex NumberConverts a complex number between rectangular (a + bi) form and polar (r∠θ) form, in either direction.Similar Triangles CalculatorScale factor and missing side lengths between two similar triangles from one matching pair of sides.Factoring CalculatorFactors a quadratic trinomial ax² + bx + c into (x − r1)(x − r2) form using its roots.Simplifying Fractions CalculatorReduces a fraction to its simplest form and shows the decimal and mixed-number equivalents.Divisor CalculatorLists every divisor of a whole number, with the count and sum of divisors.Long Division CalculatorShows the full step-by-step working for long division: bring down each digit, divide, subtract, repeat.Greater Than or Less Than CalculatorCompares two numbers and shows the correct inequality symbol: greater than, less than or equal to.Million in Numbers CalculatorExpands a figure written in thousands, millions, billions or trillions into its full digit form.Power of 1010 raised to any exponent, with a reference table of powers of 10 from 10⁰ to 10¹⁰.Matrix determinant (2×2 or 3×3)Determinant of a 2×2 or 3×3 matrix from its entries.2×2 matrix inverseInverse of a 2×2 matrix using the adjugate formula.2×2 matrix operationsAdd, subtract or multiply two 2×2 matrices, and scale one by a constant.Vector dot productScalar dot product of two 3D vectors, and the angle between them.Vector cross productThe perpendicular vector from two 3D vectors, and the area of the parallelogram they span.Vector magnitude & unit vectorLength of a 3D vector and the unit vector pointing the same way.Arithmetic sequenceThe nth term and the sum of the first n terms of an arithmetic sequence.Geometric sequenceThe nth term and the sum of a geometric sequence, plus the infinite sum where it converges.Complex number arithmeticAdd, subtract, multiply or divide two complex numbers, plus modulus and argument.Synthetic divisionDivides a polynomial by (x − r) and returns the quotient and remainder.Equation of a lineSlope-intercept, point-slope and standard form of the line through two points.Distance & midpoint between two points (3D)Straight-line distance and midpoint between two points in 3D space (set z = 0 for 2D).Law of sines (solve a triangle)Finds the remaining sides and angles from two angles and one side.Arithmetic in standard formAdd, subtract, multiply or divide two numbers written as a × 10ⁿ.Binomial expansionExpands (x + y)ⁿ term by term using the binomial theorem.Distance from a point to a linePerpendicular distance from a point to a line given in general form.Geometric & harmonic meanThe geometric mean and the harmonic mean of a list of positive numbers.Golden ratioSplits a length into golden-ratio proportions, or scales a rectangle side by φ.Point-Slope Form of a LineWrites the equation of a line in point-slope form from one point and the slope, and converts it to slope-intercept form.Trapezoidal RuleApproximates the area under a curve (a definite integral) from a set of x,y data points using the trapezoidal rule.Arcsin (Inverse Sine)The angle, in degrees and radians, whose sine equals the value you enter.Cubic Metres to Tonnes ConverterConvert cubic metres to tonnes and back, using an editable density for the material involved.Logarithm Laws CalculatorDemonstrates the product, quotient and power laws of logarithms on two numbers you choose.Arccos (Inverse Cosine)The angle, in degrees and radians, whose cosine equals the value you enter.Sum of Series CalculatorThe sum of the first n terms of an arithmetic or geometric series, with the nth term shown too.Decimal to Percentage CalculatorConverts a decimal to a percentage, or a percentage back to a decimal, by multiplying or dividing by 100.Vector AdditionAdds two 2D or 3D vectors component by component and gives the resultant vector and its magnitude.Point of IntersectionWhere two straight lines cross, from their slope-intercept equations, with parallel and identical lines handled.Sine, Cosine & TangentSine, cosine and tangent of an angle you enter, in degrees or radians.Engineering NotationConverts a number to engineering notation, with a multiple-of-3 exponent and SI prefix.Constant of Proportionality CalculatorFinds k in y = kx from one x-y pair, with an optional second pair to check the relationship is genuinely proportional.Antilog CalculatorFinds the antilogarithm of a value, the number a log of that size came from, in base 10 or base e.Ambiguous Case (SSA Triangle)Works out whether an angle and two sides in the SSA arrangement give zero, one or two possible triangles.Ratio simplifierReduces a ratio of two or more numbers to its simplest whole-number form.Eigenvector CalculatorEigenvalues and eigenvectors of a 2×2 matrix, from its four entries.Partial fraction decomposition (2 factors)Splits (ax+b)/((x−p)(x−q)) into simple fractions, including the repeated-root case.System of two linear equationsSolves a₁x+b₁y=c₁ and a₂x+b₂y=c₂ for x and y.Intersection of a circle and a lineWhere a line y = mx + c crosses a circle centred at (h, k).Matrix trace & transpose (2×2 or 3×3)Sum of the diagonal, and the matrix flipped over its diagonal.Hyperbolic functionssinh, cosh and tanh of a value, and their inverses.Circle equation: general to standard formConverts x²+y²+Dx+Ey+F=0 into centre-radius form.Absolute value equationSolves |ax + b| = c for x.Consecutive integers from a sumFinds n evenly-spaced integers (consecutive, even or odd) that add to a target sum.Divisibility testChecks which numbers from 2 to 12 divide a whole number evenly.Digital rootRepeatedly sums the digits of a number until one digit remains.Cubic equationReal roots of ax³ + bx² + cx + d = 0 via Cardano’s method.Eigenvalues of a 2×2 matrixThe two eigenvalues (real or complex) of [[a,b],[c,d]] from the characteristic polynomial.Solve a·bˣ = c for xUses logarithms to isolate x in an exponential equation.Rationalize a denominatorRemoves a square root from the denominator of a/(b + c√n) using the conjugate.Pythagorean triple generatorBuilds a right-triangle integer triple from two generator numbers (Euclid’s formula).Clock hand angleThe angle between the hour and minute hands at a given time.Reference & coterminal angleReduces any angle to its 0–360° coterminal angle, quadrant and reference angle.Round to the nearest fractionRounds a decimal to the nearest 1/2, 1/4, 1/8, 1/16 or any denominator you choose.Percent errorHow far a measured or estimated value is from the accepted true value.Set operationsUnion, intersection and differences of two sets of numbers.Alphabet to Numbers CalculatorConvert letters to their A1Z26 position numbers, or numbers back to letters.Perfect Cube CalculatorChecks whether a number is a perfect cube and shows the nearest perfect cubes below and above it.Ordering Decimals CalculatorSorts a list of decimal numbers into ascending or descending order.Cross Multiply Fractions CalculatorSolves a proportion a/b = c/d for the one missing value using cross-multiplication.Linear Equation SolverSolves a simple linear equation ax + b = c for x, with guards for a zero coefficient.Doubling TimeHow long it takes a quantity growing at a fixed percentage rate to double, by the exact formula and the Rule of 72.Completing the Square CalculatorRewrites ax² + bx + c as a(x − h)² + k, showing the completing-the-square steps.Matrix Rank CalculatorRank of a 2×2 or 3×3 matrix by Gaussian elimination, the number of linearly independent rows.Common Multiples CalculatorLists the first several common multiples shared by a set of numbers, built from their lowest common multiple.Number to Words ConverterTurns a number written in words like "8 billion" into a full numeral, or a numeral back into words.Triangle Number CalculatorThe nth triangular number, the sum of 1 to n, or checks whether a given number is one.Polygon area from vertices (shoelace formula)Area, perimeter and centroid of a simple polygon from its ordered vertices.Triangle incenter & inradiusIncenter coordinates and inscribed-circle radius from a triangle’s three vertices.Perfect, abundant & deficient number checkClassifies a whole number by comparing it to the sum of its own proper divisors.Amicable numbers checkTests whether two numbers form an amicable pair: each is the sum of the other’s divisors.Continued fraction expansionExpands a fraction p/q into continued-fraction terms and lists its convergents.Linear Diophantine equation (ax + by = c)Finds all integer solutions to ax + by = c using the extended Euclidean algorithm.System of three linear equations (Cramer’s rule)Solves a 3×3 system of linear equations using determinants.Vector projectionProjects vector a onto vector b in 3D (set z = 0 for 2D vectors).Distance from a point to a planePerpendicular distance from a point to a plane given as ax + by + cz + d = 0.Chinese remainder theorem (two congruences)Finds x satisfying x≡a₁ (mod n₁) and x≡a₂ (mod n₂), including non-coprime moduli.Modular multiplicative inverseFinds x such that a·x ≡ 1 (mod n), using the extended Euclidean algorithm.nth roots of a complex numberAll n complex roots of a+bi using De Moivre’s theorem, in polar and rectangular form.Multiplication CalculatorMultiplies any two numbers and shows the result, along with a small times-table around it.Combine Percentage ChangesCorrectly combines two successive percentage changes, such as two discounts or two price rises, without wrongly adding them.Equivalent Fractions CalculatorLists fractions equal in value to the one you enter, or finds the equivalent at a target denominator.Adjugate (Adjoint) MatrixThe adjugate of a 2×2 matrix, shown as its own labelled result, alongside the determinant and inverse.Bit Shift CalculatorShifts an integer left or right by a chosen number of bits, showing the result in decimal and binary.Percentage Points CalculatorThe percentage point difference between two percentages, alongside the separate percentage change figure.Cos 2 Theta CalculatorValue of cos(2θ) for any angle, using the double angle identity, with the intermediate cos(θ) and sin(θ) shown.Fibonacci sequenceThe nth Fibonacci number, the sequence around it and the sum so far.Egyptian fraction decompositionSplits a fraction into a sum of distinct unit fractions using the greedy algorithm.Linear interpolationEstimates a missing y (or x) on the straight line through two known points.Modular exponentiationComputes baseᵉˣᵖ mod m efficiently using square-and-multiply.Luhn algorithm (checksum)Validates a number sequence or computes the check digit that makes it valid.Manhattan (taxicab) distanceGrid-style distance between two points, moving only along axes.Euler's Number (e) CalculatorComputes e raised to any power, or the natural log of a number, using Euler's number e = 2.718281828.Sort Numbers CalculatorPuts a list of numbers in order from smallest to largest, or largest to smallest.Bitwise CalculatorRuns AND, OR, XOR or NOT on two integers, showing the result in both decimal and binary.Cholesky Decomposition CalculatorDecomposes a 3×3 symmetric positive-definite matrix A into L·Lᵀ, where L is lower triangular.Null space & rank of a matrixRank, nullity and a basis for the null space of a 2×2 or 3×3 matrix.Standard calculatorA plain calculator for everyday sums, with brackets, powers, roots and the order of operations shown as it works.Matrix multiplication costCompares the scalar multiplications needed by the schoolbook method, Strassen recursion and the AlphaEvolve 4x4 algorithm for an n by n product.Equal distances in a gridCounts the pairs of lattice points sitting at exactly the same distance apart, the quantity the Erdos unit distance problem asks about.Factorial divisibilityTests whether a! times b! divides n! times (a+b-n)!, the divisibility behind Erdos problem 728, using Legendre prime exponents.Bin packingPacks a list of item sizes into fixed-capacity bins by first fit and first fit decreasing, and compares both against the unavoidable minimum.Sorting comparisonsHow many comparisons sorting n items takes, from the information-theoretic floor to what merge sort and insertion sort actually spend.Cap set growth rateTurns a cap set found in one dimension into the growth rate per dimension and the size it implies in higher dimensions by the product construction.Ramsey number boundsThe Erdos-Szekeres upper bound on R(s,t), the probabilistic lower bound on the diagonal case, and how many colourings a brute-force search would face.Minimum overlap of a splitScores a split of the first 2n whole numbers into two halves by its worst shifted overlap, the quantity Erdos asked to minimise.Collatz conjecture (3n+1)Steps to reach 1 by halving even numbers and applying 3n + 1 to odd ones.Cosine similarityAngular similarity between two vectors, from −1 (opposite) to 1 (same direction).Descartes' rule of signsMaximum possible positive and negative real roots of a polynomial, from its sign changes.Sum of digitsAdds up the individual digits of a whole number in one pass (not repeated to a single digit).Order of magnitudeThe power of ten a number sits on, used to compare sizes at a glance.Unit rateSimplifies a ratio of two quantities to a rate per single unit of the second quantity.Golden rectangleFinds the sides, diagonal and area of a rectangle whose side ratio equals the golden ratio.Magic squareFinds the magic constant of an n×n magic square and builds it for odd n via the Siamese method.Discrete convolutionConvolves two finite number sequences to produce their discrete convolution sequence.Two's complementConverts a signed decimal integer to its binary two’s-complement form at a chosen bit width.Harmonic numberSums the reciprocals of the first n positive integers to give the nth harmonic number.Gamma functionEvaluates the gamma function Γ(x) for any real x, extending the factorial to non-integers.Error functionComputes the Gauss error function erf(x) and its complement erfc(x) for a given x.Involute functionFinds the involute of a pressure angle, used in gear-tooth geometry: φ = tan(α) − α.Absolute value inequalitiesSolves |ax + b| compared to c (<, ≤, >, ≥) and shows the solution in interval notation.Euler's formula for polyhedraFinds the missing vertex, edge or face count of a convex polyhedron from V − E + F = 2.Cyclomatic complexityComplexity of a control-flow graph from its edge, node and connected-component counts.Bilinear interpolationEstimates a value at a point inside a rectangular grid from the four surrounding known values.Percentage IncreaseNew value after a percentage increase, or the percentage increase between two values.Volume of Common ShapesVolume and surface area of a cube, box, sphere, cylinder or cone from its dimensions.AverageMean, sum and count for a list of numbers.TrigonometrySolves a right-angled triangle: the missing sides and angle from one angle and one known side.Fraction CalculatorAdd, subtract, multiply or divide two fractions or mixed numbers, simplified automatically.Gradient (Slope) of a LineGradient between two coordinate points, plus the equation of the line through them.SUVAT equations solverSolve any of the five SUVAT equations of motion for the two unknowns, given the other three.Midpoint between two pointsThe point exactly halfway between two coordinates.Hypotenuse from two legsThe hypotenuse of a right triangle from its two shorter sides.X out of Y as a percentageTurns any "X out of Y" ratio, such as 32 out of 40, into a percentage.

Statistics

Averages, spread, distributions, confidence intervals and correlation for data sets you paste straight in, with the formula shown every time.

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Descriptive statisticsMean, median, mode, spread and quartiles for a data set.Weighted averageAverage where each value carries its own weight.Z-score & percentileHow far a value sits from the mean, in standard deviations.Normal distribution probabilityArea under the bell curve between two points.Confidence interval for a meanMargin of error around a sample average.Required sample sizeHow many responses a survey needs.Correlation & linear regressionPearson r and the line of best fit for paired data.Binomial probabilityChance of exactly k successes in n independent trials.Probability of eventsCombines two event probabilities: and, or, neither.Odds ↔ probabilityConverts between fractional odds, decimal odds and percent.GPA / weighted gradeGrade point average across units with credit weights.Grade needed on the finalWhat the last assessment must score to hit a target.Interquartile Range (IQR)Q1, Q3 and the interquartile range for a list of numbers.Roll a D20Rolls one or more dice of a chosen size and gives the probability of the result you asked for.Binomial DistributionFull binomial probability distribution: probability of every outcome, mean, variance, standard deviation and shape.T-testOne or two-sample t-test with the t-statistic converted to a p-value and a significance verdict.Relative frequencyEach category's share of the total, and the running cumulative share, from a list of raw counts.Ascending Order CalculatorSorts a list of numbers into ascending order, with descending order and basic stats shown too.Average Percentage CalculatorSimple and sample-size-weighted average of several percentages, and why they can differ.Letter Grade Average CalculatorAverages several letter grades by converting each to a 4.0 grade-point value, then back to a letter.Relative & Absolute ErrorAbsolute error and relative error, as a decimal ratio, between a measured and true value.Range of a Data SetThe minimum, maximum and range (spread between them) for a list of numbers.Poker Odds CalculatorRough win probability from your number of outs, using the standard rule of 2 and 4 approximation.Conditional probabilityP(A given B), worked from either the joint probability of both events or a joint frequency table.Pie Chart Percentages CalculatorTurns a list of category values into the percentage share and degree angle each slice needs for a pie chart.Simpson's Diversity Index CalculatorSimpson’s Diversity Index (1-D) from a list of species or category counts, plus the underlying Simpson’s Index and its reciprocal.Roulette Odds & Payout CalculatorProbability of winning a chosen roulette bet and its payout ratio, for European (single-zero) or American (double-zero) wheels.Coefficient of variationRelative variability of a data set: standard deviation as a percentage of the mean.SkewnessSample skewness: whether the data leans left or right of the mean.Poisson probabilityChance of a given number of independent events in a fixed interval, given the average rate.Geometric probabilityChance the first success happens on a given trial, for repeated independent trials.Hypergeometric probabilityChance of drawing an exact number of successes from a finite population, without replacement.Chi-square goodness of fitTests whether observed category counts match expected counts.Cohen's d (effect size)Standardised difference between two group means, in pooled standard deviations.Margin of error (proportion)Margin of error for a survey proportion at a chosen confidence level.Relative riskCompares event risk between an exposed and an unexposed (or treated and control) group.T-statistic (one or two sample)How many standard errors a sample mean is from the reference value, or from another mean.Z-test for a proportionTests a sample proportion against a hypothesised population proportion.Expected value of a discrete distributionMean and standard deviation of a discrete random variable from its outcomes and probabilities.Outlier fences (Tukey)The IQR-based cutoffs beyond which a data point counts as an outlier.Residual CalculatorResiduals (observed minus predicted) for a data set against its least-squares regression line.Inverse Normal Distribution CalculatorGiven a target percentile, the value and z-score for a normal distribution with a stated mean and standard deviation.Critical Value CalculatorThe critical t or z value for a given significance level, degrees of freedom and tail direction.P-Hat (Sample Proportion) CalculatorSample proportion p-hat from a count of successes and a sample size, the standard notation used before a margin of error or confidence interval.Normal Approximation CalculatorMean and standard deviation of the normal approximation to a binomial distribution, with the np≥5 rule checked.CovarianceHow two variables move together, in sample or population form.Standard error of the meanHow much a sample mean is expected to vary from the true population mean.F-test for equal variancesCompares the spread of two samples using the ratio of their variances.Negative binomial probabilityChance that the rth success happens on exactly the kth independent trial.Percentile rankWhat percentage of a data set falls at or below a given value.Value at a percentileFinds the data value at any percentile using linear interpolation.Mean absolute deviationThe average distance of each data point from the mean (or median).Bayes’ theoremUpdates the probability of an event given new evidence.Class width for a histogramHow wide each bin should be, from either a target class count or Sturges’ rule.Spearman’s rank correlationMeasures a monotonic relationship between two variables using their ranks, ties included.Chebyshev’s theoremMinimum share of any data set within k standard deviations of the mean, whatever its shape.Two-proportion z-testTests whether two independent samples have significantly different proportions.Geometric meanThe geometric mean of a set of positive numbers, contrasted with the ordinary arithmetic mean.DPMO CalculatorDefects per million opportunities from a defect count, units produced and opportunities per unit, the standard Six Sigma quality metric.Dice Sum ProbabilityProbability of a target sum when rolling two or more dice together, with the full sum distribution.Drop Rate CalculatorProbability of getting at least one item drop over a number of attempts, from a per-attempt drop chance.Poker Probability CalculatorProbability and odds of being dealt a chosen poker hand from a standard 52-card, 5-card deal.Percent to Letter Grade CalculatorConverts a single percentage score to a letter grade on a common 10-point scale.Implied Probability CalculatorConverts decimal, fractional or American betting odds into the implied win probability.Lottery Odds CalculatorOdds of matching every number in a lottery draw, from the total number pool and how many are drawn.Pooled standard deviationCombines two sample standard deviations into one pooled estimate for equal-variance tests.Z-test for a single meanTests a sample mean against a hypothesised mean when the population standard deviation is knownQuartile deviationHalf the interquartile range: a robust spread measure, less sensitive to outliers than the SD.Range rule of thumb for standard deviationA quick estimate of standard deviation from just the minimum and maximum of a data set.Mean & standard deviation from grouped dataEstimates the mean and standard deviation of a frequency table using class midpoints.Empirical rule (68-95-99.7)The share of normal data expected within 1, 2 and 3 standard deviations of the mean.KurtosisSample excess kurtosis: how heavy-tailed a data set is versus a normal distribution.Average Star CalculatorOverall average star rating from a breakdown of how many 1 to 5 star reviews were left.Implied Odds CalculatorWhether a drawing hand is profitable to call once likely future winnings are added to the pot.Continuity Correction CalculatorAdjusts a discrete value by ±0.5 before converting to a z-score, for approximating a discrete distribution with the normal curve.Marks Needed to Pass CalculatorMarks needed on a remaining test to reach an overall passing percentage.Roulette Odds CalculatorWin probability, payout odds and house edge for straight-up and even-money roulette bets, European or American wheel.TRIFR CalculatorTotal Recordable Injury Frequency Rate from recordable injuries and hours worked.Diagnostic test accuracy metricsSensitivity, specificity, predictive values and accuracy from a 2×2 test result table.Birthday paradox probabilityChance that at least two people in a group share the same birthday.Bonferroni correctionAdjusts the significance threshold when running many statistical tests at once.Benford's law leading-digit checkCompares a data set's leading digits against the distribution natural data follows.One-way ANOVA (F-statistic)Tests whether three or more group means differ, from the raw data in each group.Lotto Odds CalculatorOdds of matching every main number in a lottery draw, with or without a separate bonus ball pool.McNemar's testTests whether paired binary outcomes changed, using the two discordant-pair counts.Mann-Whitney U test (Wilcoxon rank-sum)Compares two independent samples for a shift in distribution, using ranks instead of means.MidrangeThe midpoint between the smallest and largest value in a data set, a quick measure of centre.Sum of squaresTotal squared deviation of each data point from the mean, the building block of variance.Confusion matrixTurns the four counts of a binary confusion matrix into accuracy, precision, recall and F1.Youden's indexCombines a test’s sensitivity and specificity into one score of diagnostic performance.Weibull distributionComputes the PDF, CDF, mean and variance of a Weibull distribution from its shape and scale.Rayleigh distributionComputes the PDF, CDF, mean and variance of a Rayleigh distribution from its scale parameter.Fisher's exact testRuns a two-tailed Fisher exact test on a 2×2 contingency table of counts.Process capability indexCalculates Cp and Cpk from specification limits, the process mean and standard deviation.Degrees of freedomWorks out degrees of freedom for a one-sample, two-sample or chi-square test.Index of qualitative variationMeasures diversity among categorical frequencies on a 0 to 1 scale using the IQV formula.Beta distributionPDF, mean and variance of a beta distribution from its two shape parameters.Monty Hall problemWin probability from staying versus switching after the host reveals losing doors.Statistical power analysisAchieved power for a given sample size, and the sample size needed for a target power.Error propagationPropagates the uncertainty of two measurements through a sum, difference, product or quotient.p-value from a test statisticConverts a z, t, chi-square or F test statistic into a p-value, for any tail direction.Test grade / score percentageScore percentage and standard letter grade from correct answers out of total questions.Coin flip probabilityFlips a virtual coin and works out the probability of a given number of heads.Grade CalculatorOverall course grade and letter grade from a list of assignment scores and their weights.Median CalculatorThe middle value of a data set, sorted, with the position(s) used shown.

Geometry

Area, perimeter, volume and surface area for flat shapes and solids, plus coordinate geometry, triangles and the constructions built on them.

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CircleArea, circumference and diameter from any one measure.Circle sector & arcA wedge of a circle: arc length, area and chord.Triangle from three sidesArea, angles and centres via Heron’s formula.Right triangle / PythagorasThird side, angles and area of a right-angled triangle.Rectangle & squareArea, perimeter and diagonal.TrapezoidArea and perimeter of a four-sided figure with parallel sides.Parallelogram & rhombusArea from base and height, or from sides and angle.EllipseArea, perimeter (Ramanujan) and eccentricity.Regular polygonArea, angles and radii of an n-sided regular shape.SphereVolume and surface area from the radius.CylinderVolume, surface area and capacity of a tube or tank.ConeVolume, slant height and surface area.Rectangular prism & cubeVolume, surface area and space diagonal of a box.PyramidVolume and surface area of a rectangular-based pyramid.Torus (ring)Volume and surface of a doughnut shape.Distance, midpoint & slopeEverything about the line between two points.Area & volume unit scalingHow area and volume change when a shape is scaled.Perimeter of a SectorPerimeter of a circle sector from its radius and central angle: two radii plus the arc.Square Pyramid VolumeVolume of a square-based pyramid from its base side and height, with slant height shown.Surface Area of a Square PyramidTotal and lateral surface area of a square-based pyramid from its base side and height.Heptagon CalculatorArea and perimeter of a regular heptagon from its side length, apothem or circumradius.Area of a KiteArea of a kite from the lengths of its two diagonals.Volume of a CubeVolume, surface area and space diagonal of a cube from its side length.Area of Semicircle CalculatorArea, perimeter and arc length of a semicircle from its radius or diameter.Volume of a HemisphereVolume and surface area of a hemisphere (half a sphere) from its radius or diameter.Dodecagon CalculatorArea and perimeter of a regular 12-sided dodecagon from its side length, apothem or circumradius.Cross-Sectional AreaArea of a slice cut across a circular, rectangular or pipe-shaped object.Vertex Form CalculatorRewrites a quadratic from standard form into vertex form a(x-h)²+k, with the vertex shown.Diameter to Radius CalculatorConverts a circle’s diameter to its radius, or a radius to its diameter, both directions.Height of a TriangleSolves for a triangle’s height from its area and base, or the height of an equilateral triangle from its side.Hexagonal PyramidVolume and surface area of a right pyramid with a regular hexagonal base, from the base edge length and height.Rectangular Pyramid VolumeVolume of a pyramid with a rectangular base, from its length, width and height.Volume of Rectangle (Rectangular Box)Volume of a rectangular box (cuboid) from its length, width and height.Diagonal of a RectangleThe diagonal length of a rectangle from its two side lengths, using the Pythagorean theorem.Trapezium Prism VolumeVolume of a prism with a trapezium cross-section, from its two parallel sides, height and prism length.Area of QuadrilateralArea of any four-sided shape from the (x,y) coordinates of its four corners, using the shoelace formula.Complementary AngleThe complement (90° minus the angle) and supplement (180° minus the angle) of a given angle.Pixel Circle GeneratorWhich grid squares to fill to draw a circle of a given pixel diameter, row by row.Area of common shapesArea of a circle, square, rectangle or triangle from one shared calculator.Length and WidthSolves for the missing side of a rectangle from its area or perimeter and one known side.Euclidean DistanceStraight-line distance between two points in 2D or 3D from their coordinates.Volume in LitresVolume in litres of a box, tank or container from its length, width and height.Surface Area to Volume RatioSurface area, volume and the resulting surface-area-to-volume ratio for a cube, sphere or cylinder.Angle Between Two VectorsAngle between two 2D or 3D vectors from their components, using the dot product.Degrees in a TriangleThe fixed 180° angle sum of any triangle, plus a mini calculator for the third angle from two known ones.Aquarium VolumeVolume of a rectangular aquarium in litres and gallons, from its length, width and height.Triangle Centroid CalculatorThe centroid of a triangle, the balance point, from the coordinates of its three vertices.30-60-90 Triangle CalculatorAll three sides and the area of a 30-60-90 right triangle from any one known side.Isosceles Right Triangle CalculatorThe sides, hypotenuse and area of a 45-45-90 isosceles right triangle from any one known side.Decagon CalculatorArea and perimeter of a regular decagon from its side length, apothem or circumradius.Truncated Cone CalculatorVolume, slant height and surface area of a truncated cone (frustum) from its two radii and height.Lateral & Surface Area of a Trapezoidal PrismLateral and total surface area of a trapezoidal prism from its cross-section and length.Isosceles Trapezium CalculatorArea, perimeter and base angles of an isosceles trapezium from its two parallel sides and equal leg length.Second Moment of Area CalculatorSecond moment of area (and polar second moment) for a rectangle, solid circle or hollow tube cross-section.Volume of a Parallelepiped CalculatorVolume of a parallelepiped from three edge vectors sharing a common vertex, using the scalar triple product.Triangular Pyramid Surface AreaTotal surface area of a regular tetrahedron (all four faces equilateral) from its edge length.Vertical Exaggeration CalculatorHow much a cross-section or map profile stretches vertical relief compared with its horizontal scale.Hollow Cylinder Volume CalculatorVolume, wall thickness and surface area of a pipe or tube from its outer and inner radius.Diameter of a Cylinder CalculatorVolume and surface area of a cylinder from its diameter and height, without converting to radius first.Pot Volume CalculatorVolume in litres of a cylindrical pot, bucket or planter from its radius or diameter and height.Degrees Decimal Minutes (DDM) ConverterConverts a coordinate between decimal degrees and degrees decimal minutes (D° M.mmm′) format.Square in a Circle CalculatorThe largest square that fits inside a circle, or the smallest circle that fits around a square.Base of a TriangleFinds the base of a triangle from its area and height, by rearranging the area formula.Height of a Cone (from Slant Height)Finds the vertical height of a cone from its base radius and slant height, using Pythagoras.Minecraft Arch GeneratorBlock-by-block column heights for a symmetric semicircular arch of a given width in Minecraft.Hexadecagon (16-Sided Shape) CalculatorArea, perimeter and interior angle of a regular 16-sided polygon (hexadecagon) from its side length.Triangle Vertices CalculatorArea and perimeter of a triangle from the (x, y) coordinates of its three vertices, using the shoelace formula.Radius of a CylinderSolve for the radius of a cylinder from its volume and height, or from its curved surface area and height.Centroid of Rectangle CalculatorCentroid (geometric centre) of a rectangle from its width and height.Triangular Prism Surface Area CalculatorSurface area and volume of a right triangular prism from its right-angle leg lengths and prism length.Slant Height CalculatorFinds the slant height of a cone or a square pyramid from its vertical height and base measurement.Latus Rectum CalculatorFinds the latus rectum of a parabola, ellipse or hyperbola from its defining parameters.Radius of Curvature CalculatorFinds the radius of a circular arc from its chord width and its height at the middle (the sagitta).Circles around a circleHow many circles of a given radius fit around a central circle while each touches it, and how much angular slack is left over.Unit circle pointCoordinates, quadrant, reference angle and sin/cos/tan for a point on the unit circle.Perimeter of common shapesPerimeter or circumference of a rectangle, square, circle, triangle or regular polygon, from one shared calculator.Triangular prismVolume and surface area of a triangular prism from its base sides and length.CircumferenceCircumference of a circle from its radius or diameter, with area shown alongside.DiameterDiameter of a circle from its radius, area or circumference.Area of a CircleArea of a circle from its radius, diameter or circumference, plus the circumference itself.Volume of a CylinderVolume of a cylinder from its radius and height, with capacity in litres.Surface Area of a CylinderTotal and curved surface area of a cylinder from its radius and height.Triangle AreaArea of a triangle from base and height, three sides, or two sides and the included angle.Pythagoras Theorem HypotenuseSolve the Pythagorean theorem for the hypotenuse, or for a missing leg.Area of TrapeziumArea of a trapezium from the two parallel sides and the height between them.HexagonArea and perimeter of a regular hexagon from its side length, across-flats or across-corners measure.Isosceles TriangleArea, perimeter and angles of an isosceles triangle from its equal sides and base.Cone VolumeVolume of a cone from its base radius and height.Scalene TriangleArea, perimeter and angles from three sides, with a check that the triangle is scalene.Minecraft Circle GeneratorBlock-by-block grid for building a circle of a given diameter in Minecraft.RadiusRadius of a circle from its diameter, circumference or area.Sector AreaArea of a circle sector from its radius and central angle, with arc length shown alongside.Surface Area of a Triangular PrismTotal surface area of a triangular prism from its base sides and length.Triangle CalculatorSolve a triangle for its area, sides and angles from three common known-value combinations.Area of a RectangleArea of a rectangle from its length and width, with perimeter and diagonal shown alongside.Sphere VolumeVolume of a sphere from its radius, with surface area and litre capacity shown alongside.Angle of a Right TriangleFind an unknown angle of a right-angled triangle from two known sides.Circumference to DiameterConvert a circle’s circumference to its diameter, or a diameter to its circumference.Rhombus AreaArea of a rhombus from its two diagonals, or from a side length and interior angle.Diameter of a CircleRadius, circumference and area of a circle worked out from its diameter.Parallelogram AreaArea of a parallelogram from base and height, or from two sides and the included angle.Distance Formula (2D & 3D Points)Straight-line distance between two coordinate points, in a plane or in 3D space.Triangular Pyramid VolumeVolume of a triangular pyramid (tetrahedron) from its base sides and height.Pentagon ShapeArea, perimeter and angles of a regular pentagon from its side length, apothem or circumradius.Equilateral TriangleArea, perimeter, height and angles of an equilateral triangle from its single side length.OctagonArea, perimeter and angles of a regular octagon from its side length, across-flats or across-corners measure.Square Metre CalculationWork out the square metreage of a room in square metres, including an L-shaped room with an alcove.Area of a SphereSurface area of a sphere from its radius, with diameter and volume shown alongside.DiagonalDiagonal length of a rectangle, square or cube from its side lengths.