Maths calculators

Algebra, trigonometry, geometry and statistics: the working shown alongside every answer.

Maths

Percentages, fractions, algebra, number theory and trigonometry: the working shown alongside every answer.

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.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 meanTwo other kinds of average: the 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.

Statistics

Averages, spread, distributions, confidence and correlation for data sets you paste straight in.

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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.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 (Excel-consistent adjusted formula).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, or the gap between two means, is from the reference value.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.

Geometry

Area, perimeter, volume and surface area for flat shapes and solids, plus coordinate geometry.

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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.