Permutation and Combination Calculator

How to use

1. 1Pick a formula tab: Permutation P(n, r), Combination C(n, r), Factorial n!, Permutations with repetition (n^r), or Combinations with repetition.
2. 2Type n (the total number of items) and, when the formula needs it, r (the number you are choosing or arranging). Spaces, commas, and underscores between digits are accepted.
3. 3Read the exact result on the right: full integer with thousands separators, the symbolic equation, an approximate scientific notation form, and a step-by-step working.
4. 4Open the Notes section under the result for a short explanation of when to use the chosen formula and how it relates to the others.
5. 5Click any quick example chip (lottery, poker, password, scoops) to load the matching formula and inputs in one click, or use Copy full result to grab a clean text summary.

About this tool

Permutation and Combination Calculator answers the five most asked combinatorics questions in one tool: P(n, r) for ordered arrangements, C(n, r) for unordered selections, n! for the number of arrangements of all n items, n^r for permutations with repetition (independent picks where each of r positions can be any of n options), and C(n + r - 1, r) for combinations with repetition (the multiset coefficient that solves stars-and-bars problems). Pick a formula on the left, type n and r as whole numbers, and the exact answer appears on the right with the symbolic equation, a plain integer with thousands separators, an approximate scientific-notation form rounded to six significant figures, and a step-by-step working that mirrors what you would write on paper. The math runs in BigInt so even very large factorials are exact, never rounded; results that grow past five thousand digits are shown truncated for readability while the scientific form keeps the magnitude obvious. Inputs accept whole numbers up to one thousand and tolerate spaces, commas, and underscores as digit separators (1_000, 1,000, and 1 000 all parse the same). Quick example chips load common textbook scenarios in one click: a 6-of-49 lottery ticket, five-card and thirteen-card poker hands, an Olympic 100 metres podium, an eight-character lowercase password, three scoops from twelve ice cream flavors, four-digit PINs, and 10!. Each formula has its own notes panel that explains when to use it (order matters versus does not, repetition allowed or not), how it relates to the other formulas (P(n, n) = n!, C(n, r) = C(n, n - r), Pascal's identity), and concrete real-world uses (passwords, lottery odds, poker probabilities, dice rolls, integer solutions to equations, ways to deal cards, ways to seat people, ways to scoop ice cream). Useful for high-school algebra and pre-calculus homework, college discrete math and probability courses, programming and cryptography exercises that need exact factorials or binomial coefficients, board-game and lottery probability checks, and password-strength sanity checks. Everything runs locally on your device, so the numbers you type for class, assignments, or work stay in your browser.

Free to use. Works in your browser. No signup, no login.