Permutation & Combination Calculator
Calculate nPr and nCr with and without repetition, plus factorials, using exact big-number arithmetic that never rounds.
- Permutations nPr
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- Combinations nCr
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- Permutations with repetition
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- Combinations with repetition
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- Factorial n!
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- Factorial r!
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How it works
Enter how many items you have (n) and how many you pick (r) — every result updates as you type. Permutations count arrangements where the order matters, using nPr = n! ÷ (n − r)!. Combinations count selections where the order does not matter, using nCr = n! ÷ (r! × (n − r)!). If an item may be picked more than once you want the repetition variants instead: nr for ordered draws with replacement and (n + r − 1)! ÷ (r! × (n − 1)!) for unordered draws with replacement.
Every value is computed with JavaScript BigInt arithmetic, so results stay exact instead of collapsing to 1.234e+56 once they outgrow a normal number — a 1 000-item factorial comes back digit for digit. Copy the summary or download it as a text file for your homework, lottery odds or capacity planning notes. Nothing is uploaded: the whole calculator runs in your browser, with no account and no tracking of what you enter.
Frequently asked questions
What is the difference between a permutation and a combination?
A permutation counts arrangements where the order matters, so picking gold, silver and bronze medallists from 5 runners gives nPr = 5! / (5 - 3)! = 60 outcomes. A combination counts selections where the order is irrelevant, so choosing any 3 of those 5 runners for a team gives nCr = 5! / (3! x (5 - 3)!) = 10 outcomes. Every combination corresponds to r! permutations, which is exactly the factor that separates the two formulas.
When should I use the 'with repetition' results?
Use them whenever the same item can be chosen more than once. A 4-digit PIN drawn from 10 digits allows repeats and the order matters, so it is 10^4 = 10,000 possibilities — the permutations-with-repetition figure. Scooping 3 ice cream flavours from 5 tubs allows repeats but the order does not matter, which is the combinations-with-repetition figure, C(n + r - 1, r) = C(7, 3) = 35. The calculator shows all four cases at once so you can pick the one that matches your problem.
Does the calculator handle very large numbers exactly?
Yes. Every result is computed with JavaScript BigInt arithmetic instead of floating point, so 25! comes back as 15511210043330985984000000 rather than 1.5511e+25, and a digit count is shown beside any answer longer than 21 digits. Values of n and r up to 1000 are supported, which keeps even a full 1000! fast to expand. Everything runs in your browser — no server, no signup and no ads.