100 tools
Mathematics
Percentages, fractions, powers, geometry, statistics and everyday maths, each one showing the steps behind the result.
Tools in this category
- MathematicsPercentage CalculatorThe three questions people actually ask about percentages, answered at once, including the reverse ones.
- MathematicsPercentage Change CalculatorFind the percentage increase or decrease between two values, with the absolute difference.
- MathematicsRectangle Area CalculatorArea, perimeter and diagonal of a rectangle or square.
- MathematicsScientific CalculatorType a whole expression and get the answer, with brackets, powers, roots, logs and trigonometry.
- MathematicsCircle Area CalculatorArea, circumference and diameter of a circle from its radius.
- MathematicsWhat Percentage Is X of YTurn a part and a total into a percentage share.
- MathematicsRule of Three CalculatorSolve a direct proportion: if A gives B, what does C give?
- MathematicsEquation SolverFinds the real solutions of an equation in x, including ones no formula can give you.
- MathematicsRandom Number GeneratorDraws random whole numbers in a range, with or without repeats, from a seed you can publish.
- MathematicsDerivative Calculator with StepsThe exact derivative of a function, term by term, naming the rule used at each step.
- MathematicsPythagorean Theorem CalculatorFind the hypotenuse of a right triangle from the two shorter sides.
- MathematicsIntegral Calculator with StepsThe antiderivative where the form is one that can be recognised, and the definite integral either way.
- MathematicsTriangle Area CalculatorArea of any triangle from its base and perpendicular height.
- MathematicsCylinder Volume CalculatorVolume in cubic metres and litres, plus total surface area, of a cylinder.
- MathematicsMatrix CalculatorAdd, subtract, multiply, transpose or scale matrices of any size up to twelve by twelve.
- MathematicsCurve Fitting CalculatorThe best straight line, polynomial, exponential, power or logarithmic fit to your data, by least squares.
- MathematicsFraction CalculatorAdd, subtract, multiply or divide two fractions, with the answer simplified and as a decimal.
- MathematicsRatio Calculator (simplify and share)Simplify a ratio to its smallest whole numbers and split an amount between two parts.
- MathematicsLimit CalculatorWhere a function is heading, approached from both sides, with l'Hôpital's rule applied when the form is indeterminate.
- MathematicsTriangle SolverEvery side, every angle, the area and the two radii of any triangle, from whichever three measurements you have.
- MathematicsBox Volume CalculatorVolume in cubic metres and litres, plus surface area, of a rectangular box.
- MathematicsMatrix Inverse CalculatorThe inverse of a square matrix by Gauss-Jordan elimination, with the identity check that proves it.
- MathematicsRounding CalculatorThe same number by five different rounding rules, plus significant figures and the nearest multiple.
- MathematicsDecimal to Fraction CalculatorA decimal written as a fraction in lowest terms, including recurring decimals done exactly.
- MathematicsPercentage Difference CalculatorThe symmetric percentage difference between two values, plus the change in each direction.
- MathematicsQuadratic Formula Calculator with StepsThe roots of ax² + bx + c = 0 with the discriminant worked out, the factored form and the vertex.
- MathematicsTaylor Series CalculatorThe Taylor or Maclaurin polynomial of a function, with each coefficient and how far the approximation is off.
- MathematicsFraction to Decimal ConverterTurn any fraction into a decimal number and a percentage.
- MathematicsInterpolation CalculatorA value between the points you measured, by straight line and by the polynomial through all of them.
- MathematicsComplex Number Polar Form CalculatorA complex number in both forms, with its modulus, argument, conjugate, powers by De Moivre and all its n-th roots.
- MathematicsNewton-Raphson CalculatorA root of any function by Newton's method, with the full iteration table and an honest verdict on convergence.
- MathematicsCubic Equation CalculatorThe real roots of ax³ + bx² + cx + d = 0, by Cardano or the trigonometric form, with each root checked.
- MathematicsDifferential Equation CalculatorThe exact solution of a first-order linear equation with constant coefficients, with its equilibrium and time constant.
- MathematicsExponent CalculatorRaise any number to any power, including negative and fractional exponents.
- MathematicsNumerical Integration CalculatorThe area under a curve by the trapezium, midpoint and Simpson rules, with each one's error measured.
- MathematicsPrime Factorization CalculatorBreaks a number into its prime factors, with how many divisors it has and what they add up to.
- MathematicsLaplace Transform CalculatorThe transform of a function of time, term by term, using the standard table and linearity.
- MathematicsProportional Division CalculatorAn amount split between any number of shares in proportion, with the rounding handled so the total still adds up.
- MathematicsPrime Number CheckerWhether a number is prime, and the nearest prime above and below it.
- MathematicsRoot CalculatorFind the square root, the cube root or any nth root of a positive number.
- MathematicsBisection Method CalculatorA root found by repeatedly halving an interval, with every step shown and a check that the interval brackets one.
- MathematicsTrigonometry CalculatorSine, cosine and tangent of an angle given in degrees, plus the angle in radians.
- MathematicsLaw of Sines CalculatorThe missing side or angle from the sine rule, with the common ratio and the circumradius, and a warning when two triangles fit.
- MathematicsNumber Base ConverterConvert whole numbers between binary, octal, decimal and hexadecimal.
- MathematicsLaw of Cosines CalculatorThe third side from two sides and the angle between them, or any angle from the three sides, with the substitution shown.
- MathematicsSphere Volume CalculatorVolume and surface area of a sphere from its radius.
- MathematicsFibonacci CalculatorAny term of the Fibonacci sequence, the terms around it, the running total and how close the ratio has got to the golden ratio.
- MathematicsGCD and LCM CalculatorFind the greatest common divisor and the least common multiple of two whole numbers.
- MathematicsTriangle Area from Three SidesArea, perimeter and height of a triangle when you only know the three side lengths.
- MathematicsRoman Numeral ConverterWrite any number from 1 to 3999 in Roman numerals.
- MathematicsParabola CalculatorVertex, focus, directrix, latus rectum and roots of y = ax² + bx + c.
- MathematicsPercentage Error CalculatorHow far a measurement is from the true value, in percent and in absolute terms.
- MathematicsSuccessive Percentage ChangesThe real combined effect of two percentage changes applied one after the other.
- MathematicsLinear Equation SolverSolve ax + b = c for x, with the answer substituted back as a check.
- MathematicsLogarithm CalculatorLogarithm in any base, plus the natural logarithm and the base-2 logarithm.
- MathematicsPrism Volume CalculatorVolume and surface area of a prism whose base is a regular polygon — triangular, square, hexagonal or any other.
- MathematicsDistance Between Two PointsStraight-line distance, midpoint and direction angle between two coordinates.
- MathematicsTrapezoid Area CalculatorArea of a trapezoid from its two parallel sides and its height.
- MathematicsVector Dot and Cross Product CalculatorDot product, cross product and its magnitude, the angle between two vectors and their lengths.
- MathematicsComplex Number CalculatorProduct, quotient and sum of two complex numbers, with the modulus and argument of the first.
- MathematicsVolume by Water DisplacementThe volume of an irregular object from how far the water rises, and its density if you also weigh it.
- MathematicsFactorial Calculatorn factorial, the number of digits it has and the value of (n−1)!.
- MathematicsArithmetic Sequence CalculatorThe nth term and the sum of the first n terms of an arithmetic progression.
- MathematicsHyperbola CalculatorFoci, vertices, eccentricity, asymptotes and latus rectum of x²/a² − y²/b² = 1.
- MathematicsMatrix Determinant CalculatorThe determinant of a square matrix of any size up to twelve, by Gaussian elimination.
- MathematicsRegular Polygon CalculatorArea, perimeter, apothem, circumradius and interior angle of any regular polygon.
- MathematicsScientific Notation CalculatorTurn a number written as m × 10ⁿ into ordinary decimal form.
- MathematicsCircle Sector CalculatorArc length, sector area, chord and perimeter of a slice of a circle.
- MathematicsCone Volume CalculatorVolume and slant height of a cone from its radius and vertical height.
- MathematicsFrustum Volume Calculator (Bucket, Pot, Hopper)Volume of a truncated cone such as a bucket, a flower pot or a hopper, the volume up to any fill line, and its surface area, drawn to scale.
- MathematicsSlope and Line Equation CalculatorSlope, y-intercept, angle and x-intercept of the line through two points.
- MathematicsPlatonic Solids Calculator (Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron)Volume, surface area, the three radii (corner, edge, face) and the angle between faces of any of the five regular solids, from the edge length.
- MathematicsEllipse Area and PerimeterArea, approximate perimeter and eccentricity of an ellipse from its two semi-axes.
- MathematicsGeometric Sequence CalculatorTerm n, the sum of the first n terms and the infinite sum of a geometric progression.
- MathematicsSignificant Figures RounderRound any number to a chosen number of significant figures, with the rounding error.
- MathematicsSystem of Equations CalculatorAny number of simultaneous linear equations solved by Gaussian elimination, with the answer substituted back.
- MathematicsTorus Volume CalculatorVolume, surface area and diameters of a torus from the ring radius and the tube radius.
- MathematicsAnnulus (Ring) Area CalculatorArea of a ring from the outer and inner radius, with the wall thickness.
- MathematicsPyramid Volume CalculatorVolume, base area and slant height of a rectangular-based pyramid.
- MathematicsCircular Segment Calculator (Arch from Span and Rise)Radius, arc length, central angle and area of a circular arch or curved window from the two measurements you can actually take: the span and the rise.
- MathematicsCone Flat Pattern Calculator (Sheet Metal, Paper, Lampshades)Angle and radii of the flat piece that rolls up into a cone or a truncated cone — a funnel, a hopper, a lampshade or a paper hat — drawn to scale.
- MathematicsCubic Bézier Curve Calculator (Point and Tangent at t)The point on a cubic Bézier curve at any t between 0 and 1, with the speed and direction of the tangent there, from the four control points.
- MathematicsEllipsoid Volume and Surface Area CalculatorVolume, approximate surface area and equal-volume sphere radius of an ellipsoid from its three semi-axes.
- MathematicsDistance from a Point to a Line CalculatorThe shortest distance from a point to a line through two points, the distance to the segment between them, and the exact spot where the perpendicular lands.
- MathematicsPolygon Area from Coordinates Calculator (Shoelace Formula)Area, perimeter and centroid of a flat shape with 3 to 6 corners from the X–Y coordinates of its corners, as used for plots of land and plans.
- MathematicsTournament Matches Calculator (Round-Robin, Knockout, Double Elimination)How many matches, rounds and byes a league, a knockout cup or a double-elimination bracket needs for any number of teams.
- MathematicsTriangle Centres Calculator (Centroid, Circumcentre, Incentre, Orthocentre)The four classic centres of a triangle, its area, the radii of the inscribed and circumscribed circles and whether it is acute, right or obtuse, from the coordinates of the three corners.
- MathematicsVenn Diagram Calculator (Three Sets, Inclusion–Exclusion)How many are in at least one, in none, in exactly one or exactly two of three overlapping groups, and in each separate region of the Venn diagram.
- MathematicsCartesian, Cylindrical and Spherical Coordinates ConverterConvert a point between x–y–z, cylindrical (ρ, φ, z) and spherical (r, θ, φ) coordinates — flat polar too — and see all of them at once.
- MathematicsDerangements Calculator (Secret Santa and the Hat-Check Problem)How many ways n people can each draw somebody else's name, and the chance that a random draw works first time.
- MathematicsGamma Function Calculator (Factorial of Any Number, Beta Function)Γ(x), the factorial of non-whole numbers, ln Γ(x) and the beta function B(x, y), to about 15 significant figures.
- MathematicsGolden Ratio CalculatorSplit any length in the golden ratio, or find the long side of a golden rectangle, for layouts, frames and design.
- MathematicsHelix Length Calculator (Spiral Staircase, Coil, Handrail, Cable Wrap)Length of material along a helix — a spiral stair handrail, a coiled wire, a cable wrapped round a drum or a pole — from its diameter, pitch and height or number of turns.
- MathematicsQuadratic Sequence nth Term CalculatorThe nth-term formula an² + bn + c of a quadratic sequence from its first three terms, with any term, the next term and the sum of the first n.
- MathematicsShannon Entropy Calculator (Information in Bits, Perplexity, Gini Impurity)The entropy in bits of up to six outcomes from their frequencies or probabilities, with the maximum, the efficiency, the perplexity and the Gini impurity.
- MathematicsSpherical Cap Calculator (Volume and Surface Area of a Dome)Volume, base radius, curved and total surface area of a spherical cap — a dome, a bowl, a bubble cut by a plane — from the sphere's radius and the cap's height.
- MathematicsStadium Shape and Capsule Calculator (Running Track, Obround, Pill)Area and perimeter of a rectangle with semicircular ends — a running track, a slot or an obround — and the volume and surface of the matching 3D capsule.
- MathematicsCircle Overlap Area Calculator (Area of Intersection of Two Circles)Area of the lens where two circles overlap, from their radii and the distance between centres, with the share of each circle covered.
- MathematicsClock Angle CalculatorAngle between the hour and minute hands of a clock at any time, and how long until they next overlap.
- MathematicsCyclic Quadrilateral Calculator (Brahmagupta's Formula)Area, both diagonals, the circumscribed radius and all four angles of a four-sided figure whose corners lie on one circle, from its four sides.