Math
Free math calculators for percentages, fractions, ratios, geometry, algebra and trigonometry — each shows the formula and the working, not just an answer.
159 calculators
Fractions & percentages
Percentage CalculatorA percentage of a number, or what percent one is of another.Percent Error CalculatorPercent error between a measured value and the accepted one.Decimal to Fraction CalculatorTurn any decimal into a fraction in lowest terms.Decimal to Percent CalculatorConvert a decimal to a percentage, with the working shown.Fraction CalculatorAdd, subtract, multiply and divide fractions with simplified results.Fraction to Decimal CalculatorConvert a fraction to its decimal value, exact or rounded.Percentage Increase CalculatorPercentage increase between two values, with the method.Ratio CalculatorSimplify a ratio, with the per-one form and the decimal.Fraction to Percent CalculatorConvert a fraction to a percentage, simplified or exact.Percent to Decimal CalculatorConvert a percentage to a decimal, with the working.Percent to Fraction CalculatorConvert a percentage to a fraction in lowest terms.Adding Fractions CalculatorAdd fractions with unlike denominators, simplified.Aspect Ratio CalculatorScale an aspect ratio to a new width or height.Percentage Decrease CalculatorPercentage decrease between two values, with the method.Unit Rate CalculatorUnit rate and unit price from any quantity and cost.Equivalent Fractions CalculatorFractions equal to a given one, up to a limit.Golden Ratio CalculatorThe longer or shorter part of a golden ratio split.Marks Percentage CalculatorExam percentage from marks scored out of the total.Mixed Number CalculatorMixed number arithmetic, with the improper fraction alongside.Mixed Number to Improper Fraction CalculatorTurn a mixed number into an improper fraction.Multiplying Fractions CalculatorMultiply fractions and simplify the result.Percent Difference CalculatorPercent difference between two values, either direction.Percentage Change CalculatorPercentage change from an old value to a new one.Proportion CalculatorSolve a proportion for the missing term, with the steps.Simplify Fractions CalculatorReduce a fraction to its lowest terms and show the divisor.Subtracting Fractions CalculatorSubtract unlike fractions and show the common denominator.
Geometry
Midpoint CalculatorMidpoint of a line segment between two coordinates.Circle CalculatorRadius, diameter, circumference and area from any one of them.Cone Volume CalculatorVolume, slant height and surface area of a cone.Distance CalculatorDistance between two points, with the working shown.Endpoint CalculatorThe missing endpoint given a midpoint and the other end.Pythagorean Theorem CalculatorSolve any side of a right triangle from the other two.Surface Area CalculatorSurface area of spheres, cones, cylinders and prisms.Cylinder Volume CalculatorVolume of a cylinder, plus the areas of its ends and its curved side.Dot Product CalculatorDot product of two vectors, plus the angle between them.Hexagon CalculatorArea, perimeter and diagonals of a regular hexagon.Parallelogram Area CalculatorArea and perimeter of a parallelogram from its base, height and sloping side.Perimeter CalculatorPerimeter of common shapes from their side lengths.Rectangle CalculatorRectangle area, perimeter and diagonal from length and width.Sector Area CalculatorThe slice of a circle cut by two radii: area, arc length and chord from the angle.Segment Area CalculatorArea between a chord and its arc, from radius and angle.Sphere CalculatorA ball: any one of radius, diameter or circumference gives volume and area.Sphere Volume CalculatorHow much space a sphere takes, from its radius or diameter.Square CalculatorSide, perimeter or area of a square, plus the diagonal.Triangle Area CalculatorHalf a base times the perpendicular height above it.Aquarium Volume CalculatorTank volume in litres and gallons from its dimensions.Arc Length CalculatorThe length of the arc between two points on a circle.Area of a Trapezoid CalculatorArea of a trapezoid from its two bases and height.Central Angle CalculatorThe angle an arc subtends at the centre of its circle.Circle Area CalculatorHow much room there is inside a circle, in square units.Circumference CalculatorCircumference of a circle from its radius or diameter.Circumference to Diameter CalculatorDiameter from a circumference, and the reverse.Coterminal Angle CalculatorAngles coterminal with a given angle, positive or negative.Cuboid Volume CalculatorVolume and surface area of a rectangular box.Ellipse CalculatorEllipse area, perimeter and eccentricity from its axes.Equilateral Triangle CalculatorArea, height and perimeter of an equilateral triangle.Heron's Formula CalculatorTriangle area from three side lengths, by Heron's formula.Isosceles Triangle CalculatorArea, height and angles of an isosceles triangle.Octagon CalculatorArea, perimeter, apothem and three diagonals of an octagon.Pentagon CalculatorPentagon area, perimeter, apothem and golden-ratio diagonal.Polygon CalculatorGive the number of sides; get the area, perimeter and angles.Pool Volume CalculatorPool volume and the water needed to fill it.Pyramid Volume CalculatorVolume of any pyramid: base area times height over three.Reference Angle CalculatorThe reference angle for any angle in any quadrant.Rhombus Area CalculatorArea of a rhombus from its diagonals or a side and angle.Rhombus CalculatorArea, diagonals and height from one side and one angle.Rise Over Run CalculatorSlope, angle and percent grade from two points.Square Area CalculatorOne side in, the area out, with the formula.Trapezoid CalculatorTrapezoid area, perimeter and height from its sides.Triangle CalculatorThe third side, angles and area from two sides and an angle.Triangle Height CalculatorHeight above a given base, worked back from the area.Triangle Perimeter CalculatorPerimeter of a triangle from its three sides.Triangular Prism CalculatorVolume and surface area of a prism with triangular ends.Unit Circle CalculatorSine, cosine and tangent of an angle, read off the unit circle.Volume of a Triangular Prism CalculatorVolume of a triangular prism: base area times length.
Number bases
Binary CalculatorAdd, subtract, multiply and divide binary numbers.Hex CalculatorArithmetic on hexadecimal numbers, with decimal equivalents.Binary to Decimal ConverterConvert binary to decimal, with the place values.Binary to Hex ConverterConvert binary to hexadecimal, four bits at a time.Decimal to Binary ConverterHalve a decimal integer into binary, with each step shown.Decimal to Hex ConverterDivide a decimal integer by sixteen, showing the letters.Hex to Binary ConverterExpand each hexadecimal character into its four bits.Hex to Decimal ConverterAdd up the powers of sixteen a hex number is made of.
Algebra
Exponent CalculatorRaise a number to any power, including negative exponents.Half-Life CalculatorHow much is left after a given time, and how many half-lives.Quadratic Formula CalculatorRoots of a quadratic, including complex ones.Root CalculatorAny nth root of a whole number, exact and rounded.Slope CalculatorSlope of a line from two points or from an equation.Exponential Growth CalculatorExponential growth or decay from a rate and time.Log CalculatorLogarithms in any base, plus natural and common logs.Square Root CalculatorSquare root of any number, simplified and decimal.Absolute Value CalculatorA number's absolute value, plus its opposite.Antilog CalculatorThe number a logarithm came from, at any base.Average Rate of Change CalculatorAverage rate of change of a function over an interval.Completing the Square CalculatorThe completed-square form of a quadratic, and its vertex.Convolution CalculatorConvolution of two sequences, by index and total.Cube CalculatorCube of a number, and the number it came from.Cube Root CalculatorCube root of a number, including negative inputs.Cube Volume CalculatorVolume and surface area of a cube from its side.Doubling Time CalculatorTime for a quantity to double at a fixed growth rate.Error Function CalculatorValues of the error function and its complement.Factorial CalculatorFactorial of a number, with trailing zeros and digits.FOIL CalculatorMultiply two binomials with the FOIL method.Linear Interpolation CalculatorInterpolate a value between two known points.Long Addition CalculatorAdd whole numbers column by column, with carries shown.Multiplication CalculatorMultiply whole numbers or decimals with the steps.Point Slope Form CalculatorPoint-slope equation of a line from a point and slope.Radical CalculatorSimplify radicals and combine like terms.Scientific CalculatorEvaluate expressions with powers, roots and trigonometry.Sequence CalculatorTerms and sums of arithmetic and geometric sequences.Slope Intercept Form CalculatorThe y = mx + b equation of a line through two points.Subtraction CalculatorThe difference of whole numbers, with every borrow shown.Vertex Form CalculatorThe vertex equation y = a(x - h)² + k of a parabola.
Number theory & rounding
GCF CalculatorEvery common divisor of two to ten numbers, and the largest.LCM CalculatorThe first four common multiples of two to ten numbers.LCD CalculatorLowest common denominator for a set of fractions.Long Division CalculatorLong division step by step, with the remainder.Remainder CalculatorQuotient and remainder, under either sign convention.Rounding CalculatorRound to any place value or number of significant figures.Base CalculatorAdd, subtract, multiply and divide in any number base.Euclidean Algorithm CalculatorGCD by the Euclidean algorithm, step by step.Factor CalculatorAll factors of a number, and its factor pairs.Fibonacci CalculatorFibonacci terms up to a position, and the golden ratio.Least to Greatest CalculatorSort a list of numbers, and show the smallest and largest.Modulo CalculatorA residue that is never negative, whatever the signs are.Pascal's Triangle CalculatorRows of Pascal's triangle, and the binomial coefficients.Prime Factors CalculatorPrime factorization of a number, written with exponents.Prime Number CalculatorWhether a number is prime, and the nearest primes.Round to the Nearest Cent CalculatorRound a money amount to the nearest cent.
Averages
Weighted Average CalculatorWeighted average where each value carries its own weight.Geometric Mean CalculatorGeometric mean of a data set, for rates and ratios.Mean CalculatorArithmetic mean, with the sum and the division written out.Harmonic Mean CalculatorHarmonic mean of a set of numbers, with the working.
Scientific notation
Scientific Notation CalculatorConvert to and from scientific notation, with arithmetic.Standard Form CalculatorConvert between standard form and ordinary numbers.Expanded Form CalculatorWrite a number in expanded form, digit by digit.Place Value CalculatorThe place value of every digit in a number.Sig Fig CalculatorCount significant figures and round to a set number.
Trigonometry
Right Triangle CalculatorSolve a right triangle from two sides or a side and angle.Trigonometry CalculatorSine, cosine and tangent of any angle, in degrees or radians.Cosine CalculatorCosine of an angle in degrees or radians.Cotangent CalculatorCotangent of an angle in degrees or radians.Double Angle CalculatorDouble angle identities for sine, cosine and tangent.Half Angle CalculatorHalf angle identities for sine, cosine and tangent.Inverse Cosine CalculatorAngle from a cosine value, in degrees or radians.Inverse Sine CalculatorAngle from a sine value, in degrees or radians.Inverse Tangent CalculatorAngle from a tangent value, in degrees or radians.Law of Cosines CalculatorFind the three angles of a triangle from its three sides.Law of Sines CalculatorSolve a triangle with the law of sines and check the cases.Sine CalculatorSine of an angle in degrees or radians, with the quadrant.Tangent CalculatorTangent of an angle in degrees or radians.
Vectors & matrices
Angle Between Two Vectors CalculatorAngle between two vectors, from their dot product.Cross Product CalculatorCross product of two vectors, and its magnitude.Matrix CalculatorAdd, multiply and invert matrices, with determinants.Unit Vector CalculatorUnit vector in the direction of a given vector.Vector Addition CalculatorAdd or subtract vectors, and find the resultant.Vector CalculatorVector magnitude, direction and components.Vector Magnitude CalculatorLength of a vector in two or three dimensions.Vector Projection CalculatorProjection of one vector onto another, scalar and vector.
Other categories
Every calculator on CalcMax, grouped by what you are trying to work out.
FinanceLoans, mortgages, interest, tax and investment returns.PhysicsMotion, forces, electricity, thermodynamics and optics.Health & FitnessBMI, calories, body fat, heart rate and nutrition targets.StatisticsAverages, standard deviation, probability and grade curves.Date & TimeAge, date differences, durations, time zones and conversions.ConstructionConcrete, gravel, mulch, paint, tile and square footage.BiologyGenetics, populations, microbiology and animal dosing.SportsPace, splits, running and cycling performance metrics.ChemistryMolarity, dilutions, reactions and stoichiometry.Food & CookingRecipe scaling, baking ratios, cooking conversions.ElectronicsOhm's law, resistors, wire gauge, batteries and signals.AutomotiveFuel cost, gas mileage and trip planning.OtherBra sizing and random password generation.