160 tools

Math, geometry and statistics

160 free math, geometry and statistics tools, all running in your browser with no sign-up.

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Percentage of a number calculatorFind any percentage of a number, such as 15% of 200, and see the decimal multiplier used in the calculation.
What percent is X of Y calculatorFind what percentage one number is of another, such as your score out of the full mark or progress toward a target.
Percent change calculatorCalculate the percentage increase or decrease from an old value to a new one, with the difference and direction.
Percent difference calculatorCalculate the percent difference between two positive values relative to their average, with neither one treated as the base.
Reverse percentage calculatorFind the original value before a known percentage increase or decrease, such as a price before tax or before a discount.
Increase or decrease a number by a percentageAdd a percentage to a number or take it away, and get the new value and the change, such as a 10% salary raise.
Successive percentage change calculatorCombine up to 4 percentage changes in a row, rises or falls, into one net percentage and a final value.
Percent error calculatorCalculate the percent error between a measured or estimated value and a known true value, plus the absolute error.
Average of percentages calculatorWork out the correct average of several percentages, weighted by the size of each group, and compare it with the plain mean.
Percent to fraction converterTurn any percentage into a fraction in lowest terms and a decimal, such as 12.5% to 1/8, including repeating decimals.
Ratio simplifierReduce a ratio of two or three terms to its smallest whole numbers, such as 12:18 to 2:3, with the 1:n form and each share.
Ratio scalerScale a ratio up or down while keeping it in proportion once you know one term, such as scaling a 2:3:5 mix.
Proportion calculator (rule of three)Solve for the unknown in the proportion A:B = C:X by cross multiplication, such as the price of 6 kg when 2 kg cost 5.
Divide an amount by a ratioSplit an amount or quantity between several parties in a given ratio, such as sharing 1000 between two partners at 2:3.
Fraction calculatorAdd, subtract, multiply or divide two fractions and get the answer in lowest terms, as a mixed number and as a decimal.
Fraction simplifierReduce any fraction to lowest terms by dividing by the greatest common divisor, and see it as a mixed number and a decimal.
Fraction to decimal converterConvert any fraction to an exact decimal with the repeating part shown in brackets, such as 1/6 = 0.1(6), plus the percentage.
Decimal to fraction converterConvert any terminating or repeating decimal to a fraction in lowest terms and a mixed number, such as 0.75 = 3/4 and 0.(3) = 1/3.
Mixed number to improper fractionConvert a mixed number such as 2 1/3 into an improper fraction such as 7/3 in lowest terms, with its decimal value.
Improper fraction to mixed numberConvert an improper fraction such as 7/3 into a mixed number such as 2 1/3, with the whole part and remaining fraction in lowest terms.
Quadratic equation solverSolve any quadratic equation ax² + bx + c = 0 with the quadratic formula, showing the discriminant, root type and parabola vertex.
Linear equation solverSolve a one-variable linear equation of the form ax + b = cx + d, with the simplified form and the no-solution and infinite-solution cases.
System of 2 linear equations solverSolve a system of two linear equations in x and y using Cramer's rule, with the determinant and detection of no or infinitely many solutions.
System of 3 linear equations solverSolve three linear equations in x, y and z with Cramer's rule, showing the determinant and whether the solution is unique, missing or infinite.
Exponent calculatorRaise any number to a whole, negative or fractional power and see the result in scientific notation for very large or small values.
Logarithm calculator (any base)Find the logarithm of any positive number to base 10, 2, e or a base you choose, plus its natural and common logarithms.
Nth root calculatorCalculate the square, cube or any nth root of a number, including odd roots of negative numbers, with a check of the result.
Polynomial evaluatorEvaluate a polynomial at any x with Horner's method, showing the written polynomial, its degree and the derivative value at that point.
Slope and line equation from two pointsEnter two points to get the slope, the line equation in y = mx + b form, the y-intercept and the angle in degrees. Vertical lines work too.
Distance between two points calculatorCalculate the distance between two points in the plane or in 3D space with the distance formula, plus coordinate differences and squared distance.
Midpoint calculatorFind the midpoint between two points in the plane or in 3D space, along with the length of the segment joining them.
Linear inequality solverSolve a first-degree inequality ax + b <, ≤, > or ≥ c, flipping the sign when dividing by a negative, and show the answer in interval notation.
Absolute value equation solverSolve the absolute value equation |ax + b| = c by splitting it into two cases, handling a negative or zero right side correctly.
Cubic equation solverSolve the cubic equation ax³ + bx² + cx + d = 0 and find its three real or complex roots, with the discriminant and root type.
Point-slope form calculatorWrite the equation of a line from its slope and one point, in point-slope and slope-intercept forms, with both axis intercepts.
Parallel and perpendicular line calculatorFind the lines parallel and perpendicular to a given line through a point, plus the distance from that point to the original line.
Completing the square calculatorConvert ax² + bx + c to vertex form a(x - h)² + k by completing the square, with the vertex and which way the parabola opens.
Quadratic inequality solverSolve a second-degree inequality ax² + bx + c compared with zero using sign analysis, shown as inequalities and in interval notation.
Absolute value inequality solverSolve the absolute value inequality |ax + b| less than or greater than c by turning it into a compound inequality, with interval notation.
Exponential equation solverSolve the exponential equation a × bˣ = c for the unknown exponent x with logarithms, such as how many periods it takes a value to double.
Circle area and circumference calculatorFind the area, circumference and diameter of a circle from its radius or diameter, with results labelled in your chosen unit.
Circumference to diameter calculatorEnter the circumference of a circle to get its diameter, radius and area. Handy for measuring trees, poles and pipes with a tape.
Circle radius from area calculatorWork out the radius, diameter and circumference of a circle when you only know its area, for example a round garden of a set size.
Rectangle area and perimeter calculatorCalculate the area, perimeter and diagonal of a rectangle from its length and width, for rooms, plots, boards and screens.
Rectangle diagonal calculatorEnter any two of length, width and diagonal to find the third, plus the area and diagonal angle. Useful for screens and squaring corners.
Square area, perimeter and diagonal calculatorGet the area, side, perimeter and diagonal of a square from any one of them: side, diagonal, area or perimeter.
Triangle area calculator (base and height)Find the area of any triangle from its base and the perpendicular height to that base, using half base times height.
Heron's formula triangle area calculatorCalculate a triangle's area and perimeter from its three sides with Heron's formula, and see its type by sides and angles.
Triangle area from two sides and included angleFind a triangle's area from two sides and the angle between them, plus the third side and perimeter by the law of cosines.
Equilateral triangle calculatorFrom the side length alone, get an equilateral triangle's area, height, perimeter, inradius and circumradius.
Trapezoid area calculatorCalculate the area of a trapezoid from its two parallel bases and height, with the midsegment and the perimeter if you add the legs.
Parallelogram area calculatorCalculate a parallelogram's area, perimeter, acute angle and both diagonals from its base, side and perpendicular height.
Rhombus area calculatorFind the area of a rhombus from its two diagonals, along with its side, perimeter, height and acute angle.
Triangle inradius and circumradius calculatorFind the radius of a triangle's inscribed circle and of the circle through its vertices from the three sides, with each circle's area.
Regular polygon area calculatorFind the area and perimeter of any regular polygon, such as a hexagon, octagon or pentagon, from the side count and length.
Ellipse area and perimeter calculatorCalculate the area, exact perimeter and eccentricity of an ellipse (oval) from its semi-major and semi-minor axes.
Circle sector area calculatorCalculate the area of a circle sector, its arc length, perimeter and chord from the radius and the central angle in degrees.
Arc length calculatorWork out the arc length of a circle from the radius and central angle in degrees or radians, with the angle converted and the share of the circle.
Annulus (ring) area calculatorFind the area of the ring between two concentric circles from the outer and inner radius, such as a path around a fountain or a pipe section.
Circular segment area calculatorFind the area of a circular segment between a chord and an arc, plus the chord, arc and segment height, from the radius and central angle.
Cube volume and surface area calculatorFind the volume, total surface area, face diagonal and space diagonal of a cube from its edge length, plus liters.
Cuboid (rectangular prism) volume calculatorCalculate the volume, total surface area and space diagonal of a box or rectangular prism from length, width and height.
Sphere volume and surface area calculatorCalculate the volume, surface area and great circle circumference of a sphere from its radius or diameter, plus liters.
Hemisphere volume calculatorFind the volume, curved surface area and total surface area (with the flat base) of a hemisphere from its radius.
Cylinder volume and surface area calculatorCalculate cylinder volume, lateral and total surface area from the radius or diameter and the height, with liters.
Cone volume and surface area calculatorFind the volume, slant height, lateral and total surface area of a right circular cone from its base radius and height.
Frustum of a cone volume calculatorCalculate the volume, slant height, lateral and total area of a conical frustum from both radii and the height.
Pyramid volume and surface area calculatorFind the volume, slant heights, lateral and total surface area of a right pyramid with a rectangular or square base.
Triangular prism volume calculatorCalculate the volume and total surface area of a triangular prism from the three triangle sides and the prism length.
Hexagonal prism volume calculatorFind the volume, base area and total surface area of a regular hexagonal prism from the hexagon side and the height.
Torus volume and surface area calculatorCalculate the volume, surface area and inner and outer diameters of a torus from its major radius and tube radius.
Capsule volume calculatorFind the volume and surface area of a capsule, a cylinder with a hemisphere on each end, from its radius and total length.
Ellipsoid volume calculatorCalculate the volume of an ellipsoid from its three semi-axes, with an approximate surface area from Thomsen's formula.
Spherical cap volume calculatorFind the volume, base radius and curved surface area of a spherical cap from the sphere radius and the cap height.
Hollow cylinder (tube) volume calculatorCalculate the material volume, inner capacity and total surface area of a tube or pipe from outer and inner radius and length.
Regular tetrahedron volume calculatorFind the volume, total surface area and height of a regular tetrahedron, a pyramid of four equilateral triangles, from its edge.
Horizontal cylindrical tank fill volume calculatorFind how much liquid is in a horizontal cylindrical tank from its diameter, length and liquid depth, in liters, m³ and gallons.
Vertical cylindrical tank volume calculatorFind the capacity of an upright cylindrical tank and the liquid in it from diameter, height and liquid level, in liters and gallons.
Rectangular tank capacity calculatorCalculate the capacity of a rectangular or cube tank and the water in it from length, width, height and water level, in liters.
Sphere radius from volume calculatorEnter a sphere volume to get its radius, diameter and surface area, with the volume given in liters or in cubic units.
Right triangle calculatorSolve a right triangle from any two known values: two sides, or a side and an angle. Get all sides, angles, area and perimeter.
Pythagorean theorem calculatorFind the missing side of a right triangle with a² + b² = c², or check whether three lengths form a right triangle, with the working shown.
Law of sines calculatorSolve a triangle with the law of sines from two angles and one side (ASA or AAS). Get the other sides, the third angle and the area.
Law of cosines calculatorFind the third side of a triangle from two sides and the included angle (SAS) using the law of cosines, plus the other two angles and the area.
SSS triangle angle calculatorEnter the three side lengths of a triangle to get all three angles in degrees, plus area and perimeter, after checking the lengths form a triangle.
SSA triangle calculator (ambiguous case)Solve a triangle from two sides and a non-included angle (SSA) and see whether it has one solution, two or none, with every side and angle.
Triangle third angle calculatorEnter two angles of a triangle to get the third angle in degrees and radians, and see whether the triangle is acute, right or obtuse.
Triangle type calculatorClassify a triangle from its side lengths: equilateral, isosceles or scalene, and acute, right or obtuse, with its largest angle.
30-60-90 triangle calculatorEnter one side of a 30-60-90 special right triangle to get the other two sides, the area and the perimeter from the 1 : √3 : 2 ratio.
45-45-90 triangle calculatorGet the sides, area and perimeter of a 45-45-90 isosceles right triangle from a leg or the hypotenuse, using the 1 : 1 : √2 ratio.
Heron's formula calculatorFind the area of any triangle from its three side lengths with Heron's formula, plus the semi-perimeter and perimeter. No height or angle needed.
Triangle median calculatorFind the lengths of all three medians of any triangle from its side lengths with Apollonius's theorem, plus the centroid distance from each vertex.
Triangle altitude calculatorFind all three altitudes of any triangle from its side lengths, the perpendicular distance from each vertex to the opposite side, plus the area.
Triangle incircle and circumcircle calculatorFind the inradius of the circle inside a triangle and the circumradius of the circle through its vertices from the three side lengths.
Trig functions calculator (sin, cos, tan)Get all six trig functions of any angle in degrees or radians: sine, cosine, tangent, cosecant, secant and cotangent.
Inverse trig calculator (arcsin, arccos, arctan)Find the angle from a sine, cosine, tangent, secant or cosecant value, in degrees, radians and as a multiple of π.
Unit circle calculatorGet the point on the unit circle for any angle as (cos θ, sin θ), with exact values like √3/2 for special angles, plus the quadrant.
Reference angle calculatorFind the reference angle of any angle in degrees or radians, the acute angle it makes with the x-axis, and the quadrant it lies in.
Coterminal angle calculatorFind coterminal angles in degrees or radians: the smallest non-negative one, the nearest negative one and a table of extra full turns.
Angle of elevation calculatorWork out the height of a building or tree from the elevation angle and distance, or the angle or the distance, allowing for eye height.
Mean, median and mode calculatorPaste a list of numbers to get the mean, median, mode, range, sum, count, minimum and maximum in one step.
Standard deviation calculatorFind the sample or population standard deviation of a list of numbers, with the variance, mean and sum of squared deviations.
Variance calculatorCalculate the sample variance and the population variance side by side from a list of numbers, with both standard deviations.
Z-score calculatorTurn a raw value into a z-score from the mean and standard deviation, and see the share of a normal distribution below and above it.
Percentile rank calculatorFind the percentile rank of a value within a data set, the share of values that fall below it, such as where your score sits in a class.
Percentile calculatorFind the value at any percentile of your data, such as the 90th, using the Excel inclusive or exclusive method, with its rank position.
Confidence interval calculatorCompute a confidence interval for a population mean from the sample mean, SD and size, using t or z at 80% to 99.9% confidence.
Margin of error calculatorWork out the margin of error for a survey or poll result from the sample size, proportion and confidence level, with finite population correction.
Sample size calculatorFind how many respondents a survey or study needs from the confidence level, margin of error, expected proportion and optional population size.
Weighted average calculatorCalculate the weighted mean of a list of values and their weights, such as course marks by credit hours or purchase prices by quantity.
Correlation coefficient calculatorCalculate the Pearson correlation coefficient r between two variables, with r squared, the p-value and the strength and direction of the link.
Linear regression calculatorGet the least-squares regression line y = a + bx from X and Y data, with slope, intercept, r squared and a prediction for a new X.
Quartile and IQR calculatorFind Q1, the median, Q3, the interquartile range and the five-number summary of any data, by the textbook method or the Excel method.
Outlier calculatorSpot outliers in your data with the 1.5 × IQR or 3 × IQR rule, and see the lower and upper fences and the quartiles used.
Geometric mean calculatorCalculate the geometric mean of a list of positive numbers, the right average for growth rates, returns and ratios that compound.
Coefficient of variation calculatorFind the coefficient of variation, the standard deviation as a percentage of the mean, to compare spread across data sets with different scales.
Standard error of the mean calculatorCalculate the standard error of the mean (SEM) from a list of sample data, with the sample standard deviation, mean and count.
Mean absolute deviation calculatorCalculate the mean absolute deviation of a list of numbers, the average distance of each value from the mean, with a table of deviations.
P-value calculatorConvert a z or t test statistic into a p-value for a left, right or two-tailed test, with the verdict at the 5% and 1% levels.
Normal distribution calculatorFind the probability that a value from a normal distribution falls below, above or between given limits, from the mean and standard deviation.
Permutation calculator (nPr)Count permutations nPr, the ordered ways to pick r items from n, with or without repetition, as an exact whole number even when it is huge.
Combination calculator (nCr)Count combinations nCr, the ways to choose r items from n when order does not matter, with or without repetition, as an exact whole number.
Factorial calculator (n!)Calculate the factorial of any whole number up to 3000 with every digit, plus its digit count, trailing zeros and scientific notation.
Binomial probability calculatorFind the probability of exactly k successes in n independent trials with success chance p, plus cumulative probabilities, mean and standard deviation.
Poisson distribution calculatorFind the probability of exactly k events in an interval when the average rate λ is known, with cumulative probabilities both ways.
Negative binomial distribution calculatorFind the chance that the r-th success lands exactly on trial k, by trial k or after it, plus the mean number of trials and standard deviation.
Expected value calculatorCalculate the expected value, variance and standard deviation of a discrete random variable from its outcomes and their probabilities.
Odds to probability calculatorConvert odds written as a : b, either in favour of or against an event, into a probability as a percentage and a decimal, plus the opposite event.
Probability to odds calculatorConvert a percentage probability into odds in favour and odds against in simplified a : b form, plus the odds ratio as a single number.
Exponential distribution calculatorFind the chance the next event happens within time x, after it or between two times, from the rate λ or the mean wait, with the median and SD.
Circular permutation calculatorCount the ways to arrange r of n items around a circle, such as seats at a round table or beads on a necklace that can be flipped, as an exact number.
Birthday paradox calculatorFind the chance that at least two people in a group of n share a birthday, and how many people it takes to pass 50%.
Coin flip streak probability calculatorFind the chance of at least one run of k heads in a row, or k of either side, somewhere in n flips of a fair or biased coin.
At least once probability calculatorFind the chance an event happens at least once in n independent tries, and how many tries you need to reach a target chance.
Hypergeometric distribution calculatorFind the chance of drawing exactly k wanted items without replacement, like cards from a deck, with cumulative probabilities and the mean.
Geometric distribution calculatorFind the chance that the first success comes on exactly trial k, within k trials or after them, plus the average number of trials.
Bayes' theorem calculatorCalculate the updated probability P(A|B) from the prior, the true positive rate and the false positive rate, such as what a positive test really means.
Two independent events probability calculatorFind the chance that two independent events both happen, at least one happens, neither happens or exactly one happens, from each event’s chance.
Word letter arrangements calculatorCount the distinct ways to arrange the letters of a word, allowing for repeated letters, in Arabic or English, with a count of each letter.
Pascal's triangle generatorGenerate Pascal's triangle up to 30 rows ready to copy, with the last row and its sum; each entry is the combination C(n, k).
GCD calculator (greatest common divisor)Find the greatest common divisor of two or more whole numbers with Euclidean algorithm steps, and see whether they are coprime.
LCM calculator (least common multiple)Find the least common multiple of two or more whole numbers with full precision, even for very large results, plus their GCD.
Prime number checkerCheck instantly whether a number up to 10^15 is prime or composite, with its smallest prime factor and the previous and next primes.
Prime factorization calculatorBreak any number up to 10^15 into its prime factors, in exponent form and full product form, with its number of divisors.
Divisors calculator (all factors of a number)List every divisor of a number up to 10^12 in order, with the divisor count, the sum of divisors and the sum of proper divisors.
Fibonacci number calculatorCompute the nth Fibonacci number exactly up to n = 2000, with its digit count and the first terms of the sequence.
Arithmetic sequence calculatorFind the nth term and the sum of the first n terms of an arithmetic sequence from its first term and common difference, with the first terms listed.
Geometric sequence calculatorFind the nth term and the sum of the first n terms of a geometric sequence, plus the infinite sum when the series converges.
Sum of series calculator (numbers, squares, cubes)Add up whole numbers, their squares or their cubes between two limits using closed formulas, exactly, for ranges up to one billion.
Matrix determinant calculatorCompute the determinant of a square matrix from 2 × 2 to 5 × 5 by cofactor expansion, and see whether the matrix is invertible.
Matrix multiplication calculatorMultiply two matrices up to 10 × 10 and get the product in aligned columns, with a dimension check before multiplying.
Modulo calculator (a mod n)Compute a mod n for positive, negative and decimal numbers, with the integer quotient and the truncated remainder that many programming languages use.
Perfect, abundant or deficient number checkerFind out whether a number up to 10^12 is perfect, abundant or deficient by comparing it with the sum of its proper divisors.
Digit sum and digital root calculatorAdd up the digits of a number of any length and get its digital root and digit count, with divisibility by 3 and 9.
Prime numbers list generator (primes in a range)List every prime between two numbers and count them with the sieve of Eratosthenes, for ranges up to one billion and 10 million wide.
Matrix inverse calculatorFind the inverse of a square matrix from 2 × 2 to 4 × 4 with the adjugate method, as exact fractions for integer matrices and as decimals.
Modular exponentiation calculator (a^b mod m)Compute a^b mod m exactly for huge exponents up to 10^15 using square-and-multiply, as used in cryptography and number theory.
Modular inverse calculatorFind the modular multiplicative inverse of a modulo m with the extended Euclidean algorithm, and verify that a × x mod m = 1.
Euler's totient function calculator φ(n)Compute Euler's totient φ(n), the count of numbers from 1 to n that are coprime to n, for any n up to 10^15 from its prime factors.
Nth prime number calculatorFind the prime at position n, up to the one millionth prime, such as the 100th prime 541, with the primes just before and after it.