Math Calculators
Free math calculators for percentages, fractions, scientific operations, statistics, and geometry. Step-by-step results you can check.
68 tools in 4 groups
Most popular
- Scientific CalculatorWork out sums with powers, roots, logs and trigonometry. Type or tap your sum, choose degrees or radians, and see each step in the right order.
- Fraction CalculatorAdd, subtract, multiply, divide, compare, order, average or estimate fractions and mixed numbers, convert fractions, decimals and percents, and see every step.
- Percentage CalculatorUse the Percentage Calculator to find a part, rate or whole, calculate percentage increase or decrease, and compare two values by percentage difference.
- Random Number GeneratorGenerate random numbers in any range, with or without repeats, or draw several sorted lottery-style tickets with a bonus-ball pool, from your browser's secure source.
Arithmetic & Algebra
- Scientific CalculatorWork out sums with powers, roots, logs and trigonometry. Type or tap your sum, choose degrees or radians, and see each step in the right order.
- Percentage CalculatorUse the Percentage Calculator to find a part, rate or whole, calculate percentage increase or decrease, and compare two values by percentage difference.
- Fraction CalculatorAdd, subtract, multiply, divide, compare, order, average or estimate fractions and mixed numbers, convert fractions, decimals and percents, and see every step.
- Exponent CalculatorWork out a power such as 2¹⁰, or find the base or the exponent, with the steps and a table of related powers.
- Logarithm CalculatorSolve log_b(x) = y for y, x or b. The steps show your numbers in the formula and then check the answer.
- Root CalculatorFind the square root, cube root or any nth root of a number, and see the root simplified by pulling out whole groups of primes.
- Ratio CalculatorSimplify, scale or solve ratios, split an amount into parts of a whole, compare unit prices, or use the golden ratio, with every step shown.
- Quadratic Formula CalculatorSolve ax² + bx + c = 0: type a, b and c to get the roots, with the discriminant, vertex, factored form and a graph of the curve.
- Complex Number CalculatorAdd, subtract, multiply or divide two complex numbers step by step, and see the answer’s magnitude (size) and argument (angle).
- Arithmetic Sequence CalculatorFind an arithmetic sequence’s nth term, finite sum and first terms from the initial value and common difference.
- Geometric Sequence CalculatorFind a geometric sequence’s nth term and finite sum from its starting term, common ratio and term count.
- Vector CalculatorCalculate dot product, sum, difference and angle for matching vectors, plus the cross product for three-dimensional vectors.
- Matrix CalculatorCalculate determinants, inverses (Gauss–Jordan), ranks, powers and scalar multiples, or add, subtract, multiply and transpose matrices, with exact fractions.
- Percentage Points CalculatorFind the gap between two percentages in percentage points, and the relative percentage change, with every step shown.
- Percent Error CalculatorCompare a measurement with an accepted reference and see absolute error, signed error and percentage error.
- Absolute Value CalculatorFind the absolute value of a number (its distance from 0), or the distance between two numbers, with every step shown.
- Cubic Equation CalculatorSolve a cubic equation ax³ + bx² + cx + d = 0. See all three roots (including complex ones), what kind of roots they are, and every step.
- FOIL CalculatorMultiply two brackets (ax + b)(cx + d) with the FOIL method and see all four products, or factor a difference of two squares and check it.
- Long Multiplication CalculatorWork through long multiplication one partial product at a time, or use the lattice grid, long addition with carrying, long subtraction with borrowing, or negative-number rules.
- Exponential Growth CalculatorWork out exponential growth or decay: find the final value, starting value, rate or time, and see the doubling time or half-life.
- PPM CalculatorChange any parts-per amount into ppm, ppb, ppt, percent, per mille, per myriad or a plain fraction.
- Adding MachineEnter amounts one per line, like on a desk adding machine. Each line updates the running total, S prints a subtotal and T prints a total, and the whole tape downloads as CSV.
- Convolution CalculatorEnter two finite sequences to get their discrete convolution, with every output sample written out as its sum of products. Switch to circular convolution for a chosen period N.
- Diamond Problem CalculatorFill in any two corners of a diamond problem and get the other two. When you know the product and the sum, the two factors come from a quadratic equation, and the steps show how.
- System of Equations CalculatorSolve two or three linear equations at once, with determinants and substituted steps. Coin and age word-problem modes turn the story into equations and solve them the same way.
Number Theory
- LCM CalculatorFind the smallest number that every number in your list divides into exactly. See the multiples, the prime factors and how each number fits into the answer.
- GCF CalculatorFind the biggest whole number that divides every number in your list exactly, then use it to make a ratio or fraction simpler.
- Factor CalculatorList every number that divides a whole number exactly, see its factor pairs, and break it into primes.
- Prime Factorization CalculatorBreak a whole number into the primes that multiply to make it, step by step, or list the first N primes or every prime between two numbers.
- Scientific Notation CalculatorNormalize a number into a coefficient and power of ten, expand scientific notation back to a decimal, or do arithmetic on two numbers with renormalization steps.
- Significant Figures CalculatorCount which digits are significant and why, round a measurement to a set number of significant figures, or apply the addition and multiplication rules to two values.
- Rounding CalculatorRound a number to decimal places, tens or a chosen multiple. Pick a rounding method, see the kept digit and the discarded part, and compare all eight methods.
- Long Division CalculatorDivide exactly, step by step. Choose a whole-number quotient with remainder or a decimal quotient; repeating decimals are detected and their repeating block is shown.
- Binary and Hex CalculatorConvert whole numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36, exactly, with every step shown.
- Big Number CalculatorAdd, subtract, multiply, divide and more with very large or very precise numbers, keeping every digit exact and choosing how many decimal places to show.
- Binary CalculatorDo exact integer arithmetic and bitwise logic in binary, octal, decimal, hex or any base up to 36, and see every result in all four bases with its bit pattern.
- Factorial CalculatorFind the exact value of n! (n factorial) for any whole number up to 5,000, or a multifactorial such as n!!, with every step shown.
- Pascal's Triangle CalculatorBuild Pascal's triangle row by row, list any single row, or find one number C(n, k) exactly, with the rule that adds the two numbers above.
- Place Value CalculatorSee the place and value of every digit in a number, with its expanded form, powers of ten and the number in words.
- Fibonacci CalculatorFind any Fibonacci number exactly, list the sequence, check whether a number is in it, and see how the numbers link to the golden ratio.
- Multiples CalculatorList the multiples of a number, find the common multiples of several numbers, or check whether one number is a multiple of another.
Statistics & Probability
- Standard Deviation CalculatorPaste a data set to get the standard deviation, variance, mean, median, and range, with the choice between sample and population formulas and the working shown.
- Random Number GeneratorGenerate random numbers in any range, with or without repeats, or draw several sorted lottery-style tickets with a bonus-ball pool, from your browser's secure source.
- Mean, Median and Mode CalculatorCompare the average, middle value and most frequent values of your data, with sorted values and the working shown.
- Statistics CalculatorSummarize the center, spread and shape of a data set, with the mean, variance, SD and quartiles worked out from your own numbers, plus outliers and a histogram.
- Z-Score CalculatorMeasure how far a value is from the mean in standard deviations, or work backward from a z-score or normal percentile.
- Permutation and Combination CalculatorCount the ways to arrange items when order matters (permutations) or to choose a group when it does not (combinations), with and without repeats.
- Probability CalculatorFind the chance of two events happening together, either one, or neither, or the chance of a number of successes in repeated tries, with every step shown.
- Linear Regression CalculatorFit a least-squares line to paired observations and calculate slope, intercept, R² and a prediction at a selected x value.
- Weighted Average CalculatorFind an average where some values count more than others. Enter the values and their weights; the weights do not need to add up to 100.
- Sample Size CalculatorFind how many survey answers you need from your confidence level, margin of error, population size and response rate.
- Confidence Interval CalculatorFind the range that probably holds the true average or proportion, from your sample and a confidence level, with every step shown.
- P-value CalculatorConvert a z or t statistic into a tail probability, or work backwards from a probability to a statistic. Compare regions and understand what the result means.
- Percentile CalculatorPaste a data set to find the value at any percentile, or the percentile rank of a particular value, and see which definition is being used and how it compares with Excel.
- Stem-and-Leaf Plot CalculatorPaste a data set to build a stem-and-leaf plot that keeps every value visible, with an automatic or chosen leaf unit, optional split stems and a key.
- Odds CalculatorConvert any odds format into the others and into an implied probability, then see the profit and total return on a stake at those odds.
Geometry
- Triangle CalculatorEnter any three values of a triangle — sides, angles or a mix, with at least one side — to solve every side and angle, the area, perimeter, heights, inradius and circumradius, with the law of sines or cosines worked through and the ambiguous case reported.
- Area CalculatorFind the area of 13 plane shapes in mixed units, see the perimeter, diagonals and other measurements, or solve for a missing dimension from a known area.
- Circle CalculatorCalculate radius, diameter, circumference and area from any one known circle measurement, with unit conversion.
- Volume CalculatorFind the volume and surface area of 14 solids in mixed units, see slant heights, diagonals and lateral areas, or solve for a missing dimension from a known volume.
- Pythagorean Theorem CalculatorUse the Pythagorean Theorem Calculator to find a missing right-triangle side from two known sides, plus angles, area and perimeter.
- Right Triangle CalculatorSolve a right triangle from two independent side, acute-angle or altitude measurements, including ambiguous solutions.
- Slope CalculatorFind slope, line equation, intercept and inclination from two points or a point and slope, plus distance and midpoint for two points.
- Distance CalculatorFind the distance between two 2D or 3D points with worked steps, plus the midpoint and slope, or estimate great-circle distance from latitude and longitude.
- Surface Area CalculatorCalculate the surface area of twelve closed solids, including prisms, frustums, spherical caps and ellipsoids, with lateral and base areas and every step shown.
- Tank Volume CalculatorEnter a tank's inside dimensions and the depth of liquid to get its full capacity, the volume it holds now and the fill percentage, for vertical and horizontal tanks.
- Trigonometry CalculatorEnter an angle to get all six trigonometric functions at once, with exact forms such as √3/2 for special angles, or work backwards with asin, acos, atan and the other inverses.
- DMS CalculatorConvert an angle or a latitude/longitude between decimal degrees and degrees-minutes-seconds (D° M′ S″), including negative values and hemisphere letters.