Math
Percentages, fractions, statistics, and geometry.
From percentages and fractions to statistics, geometry and sequences, these math calculators show the full working, not just the answer. Each lists the formula it uses and a worked example, so they double as a way to check your own steps.
60 calculators
Area Calculator — square, rectangle, triangle, circleFind the area of a square (a²), rectangle (a×b), triangle (½ base × height) or circle (πr²). Pick a shape and enter its dimensions.Arithmetic Sequence Calculator — nth term and sumFind the nth term and the sum of an arithmetic sequence from the first term and common difference. For a₁=2, d=3, the 10th term is 29 and the first 10 terms sum to 155.Average Calculator — arithmetic, geometric & harmonic meanFind the average of a list of numbers — the arithmetic mean, geometric mean, harmonic mean and median. Enter numbers separated by commas or spaces. For 2, 4, 4, 4, 5, 5, 7, 9 the arithmetic mean is 5.Binomial Distribution Calculator — probability of k successes in n trialsFind the probability of exactly k successes in n independent trials with success probability p: P = C(n,k) × p^k × (1−p)^(n−k). Enter n, k and p.Calculator — free online basic calculatorA free online basic calculator for everyday arithmetic. Add, subtract, multiply, and divide with memory keys, following the standard order of operations (2 + 3 × 4 = 14).Circle Calculator — area, circumference and diameter from radiusFrom a circle's radius, find its area (πr²), circumference (2πr) and diameter (2r). Enter the radius — for r = 5, area ≈ 78.54 and circumference ≈ 31.42.Confidence Interval Calculator — for a mean (z-interval)Find the confidence interval for a mean: x̄ ± z·σ/√n. Enter the sample mean, standard deviation and size, pick 90/95/99%, and read the margin of error and bounds.Cube Root Calculator — find ∛xFind the cube root of a number, ∛x — the value whose cube equals x. Works for negatives too: ∛27 = 3 and ∛−8 = −2. Every real number has one real cube root.Decimal to Fraction Calculator — convert a decimal to a fractionConvert any decimal to a fraction in lowest terms and a mixed number. Enter a decimal to see its exact fraction. 0.75 is 3/4; 2.75 is 11/4, or 2 3/4.Descriptive Statistics Calculator — full data summaryGet a complete descriptive-statistics summary of a data set: count, sum, mean, median, mode, minimum, maximum, range, variance and standard deviation. Enter numbers separated by commas or spaces.Distance Calculator — distance between two pointsFind the straight-line distance between two points with the distance formula: d = √((x2 − x1)² + (y2 − y1)²), the Pythagorean theorem in coordinates.Exponent Calculator — raise a base to a powerCompute a base raised to an exponent, base^n — including negative exponents (reciprocals) and fractional exponents (roots). Enter a base and a power.Factorial Calculator — compute n! for any whole numberCompute the factorial n! = 1 × 2 × 3 × ... × n, the product of all positive integers up to n, with 0! = 1. Enter a whole number to get its factorial.Fraction Calculator — add, subtract, multiply, divide fractionsAdd, subtract, multiply or divide two fractions and get the answer in lowest terms, as a mixed number and as a decimal. 1/2 + 1/3 = 5/6.Fraction to Decimal Calculator — convert a fraction to a decimalConvert a fraction to a decimal by dividing the numerator by the denominator: a/b = a ÷ b. Enter a numerator and denominator, like 3/4 = 0.75.Fraction to Percent Calculator — convert a fraction to a percentageConvert any fraction to a percentage and a decimal. Enter a numerator and denominator to see the percent. 3/4 is 75%; 1/3 is about 33.33%.GCF Calculator — greatest common factor of two numbersFind the greatest common factor (GCF), also called the greatest common divisor, of two whole numbers — the largest number that divides both exactly.GPA Calculator — grade point averageCalculate your GPA from letter grades and credit hours. GPA is the credit-weighted average of grade points on the 4.0 scale. For B (3 credits), A- (4), C (2) and C (3) the GPA is about 2.81.Grade Calculator — your weighted course gradeWork out your weighted course grade from each assignment or category score and its weight — the weighted average, with the steps shown. Enter scores and weights.Hex / Decimal / Binary Converter — number base converterConvert a decimal number to binary, octal and hexadecimal. Enter a whole number to see all three bases. 255 is FF in hex, 377 in octal and 11111111 in binary.LCM Calculator — least common multiple of two numbersFind the least common multiple (LCM) of two whole numbers — the smallest number both divide into — computed as their product divided by the greatest common factor.Logarithm Calculator — log of a number to any baseCompute the logarithm of a number to any base: log_base(x) = ln(x) ÷ ln(base). It answers what power the base must be raised to to get x — log₁₀(1000) = 3.Mean, Median, Mode Calculator — measures of central tendencyFind the mean, median and mode of a list of numbers. Enter your data separated by commas or spaces. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the median is 4.5 and the mode is 4.Midpoint Calculator — midpoint between two pointsFind the midpoint between two points — the point halfway between them — by averaging the coordinates: ((x1 + x2) ÷ 2, (y1 + y2) ÷ 2).Mixed Number to Fraction Calculator — convert to an improper fractionConvert a mixed number to an improper fraction and a decimal. Enter the whole number, numerator and denominator. 2 1/2 becomes 5/2, or 2.5.Modulo Calculator — remainder of a divisionFind a mod n — the remainder when one number is divided by another — plus the quotient. Enter a dividend and divisor. 17 mod 5 is 2, with a quotient of 3.Nth Root Calculator — find the nth root of a numberFind the nth root of a number, x^(1/n) — the value that raised to the power n gives x. Generalises square and cube roots: the 5th root of 32 is 2.Percent Error Calculator — measured vs true valueCalculate percent error between a measured value and the true value: |measured − actual| ÷ |actual| × 100. Enter both to get the error as a percentage.Percent to Fraction Calculator — convert a percentage to a fractionConvert any percentage to a fraction in lowest terms and a mixed number. Enter a percent to see its fraction. 75% is 3/4; 150% is 3/2, or 1 1/2.Percentage Calculator — what percent one number is of anotherWork out what percent one number is of another: percentage = part ÷ whole × 100. Enter a part and a whole to get the exact percentage, with the steps shown.Percentage Change Calculator — increase or decrease between two numbersCalculate the percentage change from one number to another: change = (new − old) ÷ old × 100. Positive is an increase, negative a decrease — steps shown.Percentage Increase Calculator — increase or decrease a number by a percentIncrease or decrease a number by a percentage: result = value × (1 + percent ÷ 100). Enter a value and a percent (negative to decrease) to get the new amount.Percentage of a Number Calculator — what is X% of YFind what a percentage of a number is: amount = percent ÷ 100 × number. Enter a percent and a number to get the result, like 15% of 80 = 12, steps shown.Perimeter Calculator — square, rectangle, triangle, circleFind the perimeter of a square (4a), rectangle (2(a+b)), triangle (a+b+c) or circle (circumference 2πr). Pick a shape and enter its dimensions.Permutation & Combination Calculator — nPr and nCrCalculate permutations (nPr, order matters) and combinations (nCr, order doesn't) of r items from n: nPr = n!/(n−r)!, nCr = n!/(r!(n−r)!). Both shown together.Prime Factorization Calculator — factor a number into primesBreak any whole number into its prime factors. Enter a number to see its prime factorization as a product of prime powers, with the count of distinct primes. 360 = 2³ × 3² × 5.Prime Number Checker — is a number prime?Check whether a whole number is prime — divisible only by 1 and itself — and if not, find its smallest prime factor. 17 is prime; 15 is composite (3 × 5).Probability Calculator — chance of an event from outcomesCalculate the probability of an event as favorable outcomes ÷ total outcomes, plus the complement (chance it doesn't happen). Enter the counts to get the odds.Proportion Calculator — solve a : b = c : xSolve a proportion a : b = c : x for the missing value by cross-multiplication: x = b × c ÷ a. Enter three terms to find the fourth.Pythagorean Theorem Calculator — hypotenuse from two legsFind the hypotenuse of a right triangle from its two legs using the Pythagorean theorem: c = √(a² + b²). Enter the two legs, like 3 and 4 giving 5.Quadratic Formula Calculator — solve ax² + bx + c = 0Solve a quadratic equation ax² + bx + c = 0 with the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a. Enter a, b and c to get both roots and the discriminant.Range Calculator — largest minus smallestFind the range of a data set — the largest value minus the smallest — along with the minimum, maximum and midrange. Enter numbers separated by commas or spaces. For 2, 4, 4, 4, 5, 5, 7, 9 the range is 7.Ratio Calculator — simplify a ratio to lowest termsSimplify a ratio a : b to its lowest terms by dividing both sides by their greatest common divisor, and see it as a decimal. Enter two numbers to reduce.Right Triangle Calculator — hypotenuse, area, perimeter and anglesFrom the two legs of a right triangle, find the hypotenuse (√(a²+b²)), the area (½·a·b), the perimeter and the two acute angles. Enter the legs a and b.Roman Numerals Converter — number to Roman numeralConvert any whole number from 1 to 3999 into Roman numerals. Enter a number to see its numeral using I, V, X, L, C, D and M. 2026 is MMXXVI.Rounding Calculator — round to decimal places (nearest, up, down)Round a number to any number of decimal places — to the nearest (ties to even), up (ceiling) or down (floor). Enter a value, the places and the mode.Sample Size Calculator — for estimating a meanFind the minimum sample size to estimate a mean within a target margin of error: n = (z·σ/E)², rounded up. Pick 90/95/99% confidence, enter σ and the margin.Scientific Calculator — trig, logs, powers, and rootsA free online scientific calculator with sine, cosine, and tangent (and inverses), natural and base-10 logarithms, powers, roots, factorials, π and e, parentheses, and a degrees/radians switch.Scientific Notation Calculator — convert a number to a × 10ⁿConvert a number to scientific notation, a × 10ⁿ, with the mantissa between 1 and 10 and the exponent its order of magnitude. 1234 becomes 1.234 × 10³.Significant Figures Calculator — round to N sig figsRound a number to a chosen number of significant figures — the meaningful digits from the first non-zero one. 3.14159 to 3 sig figs is 3.14; 12345 to 2 is 12000.Simplify Fractions Calculator — reduce to lowest termsReduce any fraction to its lowest terms. Enter a numerator and denominator to get the simplified fraction and its decimal value. 8/12 simplifies to 2/3.Slope Calculator — slope of a line from two pointsFind the slope of a line through two points: m = (y2 − y1) ÷ (x2 − x1), the rise over the run. Positive slopes rise, negative fall, zero is horizontal.Square Root Calculator — find √xFind the square root of a number, √x — the value whose square equals x. Handles perfect squares like 144 = 12 and irrationals like √2 ≈ 1.4142.Standard Deviation Calculator — sample and populationCalculate the sample and population standard deviation and variance of a data set. Enter numbers separated by commas or spaces. For 2, 4, 4, 4, 5, 5, 7, 9 the population standard deviation is 2 and the sample standard deviation is about 2.1381.Surface Area Calculator — cube, box, sphere, cylinderFind the total surface area of a cube (6a²), box (2(ab+bc+ca)), sphere (4πr²) or cylinder (2πr(r+h)). Pick a solid and enter its dimensions.Triangle Calculator — area from three sides (Heron's formula)Find a triangle's area, perimeter and semiperimeter from its three side lengths using Heron's formula, A = √(s(s−a)(s−b)(s−c)) with s the semiperimeter.Trigonometry Calculator — sine, cosine and tangent of an angleFind the sine, cosine and tangent of an angle in degrees. For 30°, sin = 0.5, cos ≈ 0.8660 and tan ≈ 0.5774. Tangent is undefined at 90° and 270°.Variance Calculator — sample and population varianceCalculate the sample and population variance of a data set, plus the standard deviations. Enter numbers separated by commas or spaces. For 2, 4, 4, 4, 5, 5, 7, 9 the population variance is 4 and the sample variance is about 4.5714.Volume Calculator — cube, box, sphere, cylinder, coneFind the volume of a cube (a³), box (a×b×c), sphere (4/3 πr³), cylinder (πr²h) or cone (⅓ πr²h). Pick a solid and enter its dimensions.Z-Score Calculator — standard score from value, mean and SDCalculate a z-score (standard score): z = (x − mean) ÷ standard deviation. It tells you how many standard deviations a value sits above or below the mean.