Factorial, Permutations & Combinations Calculator
Compute n!, nPr and nCr exactly with big-integer arithmetic, plus the digit count and scientific notation for numbers far too long to print. Free, no signup.
120
≈ 1.2000 × 10^2 · 3 digits
20
≈ 2.0000 × 10^1 · 2 digits
10
≈ 1.0000 × 10^1 · 2 digits
🔒 Calculated in your browser — nothing is uploaded. Exact BigInt math keeps even huge results precise.
Exact, not approximate
Enter n for the factorial, and r as well for permutations and combinations. The arithmetic uses big integers rather than floating point, so 100! is the whole 158-digit number and not a rounded one, and every digit of nCr is correct. Each answer has its own copy button.
How big it is, even when it cannot be printed
Beside every answer the page says how many digits it has and gives it in scientific notation — 1000! is ≈ 4.0239 × 10^2567, with 2,568 digits. Past ten thousand digits the middle of the number is left out on screen, because one unbroken run that long is not something a page can lay out, but Copy still takes every digit, all the way up to 20000!. Above that the size is still answered exactly: ask for 50000! or a billion factorial and you get the digit count immediately. The old version simply refused anything above a thousand, which made a question with a one-line answer into a dead end.
What nPr and nCr actually mean
Permutations count arrangements where the order matters: first, second and third places from ten runners is 10P3 = 720. Combinations count selections where it does not: a team of three from ten people is 10C3 = 120, six times fewer, because each team of three can be ordered six ways. Both labels carry that explanation on the page, so the notation does not have to be looked up somewhere else.
Frequently asked questions
What is the difference between nPr and nCr?
Order. nPr counts arrangements — first, second, third — and nCr counts selections, where a group is the same group however it is listed. nCr is always nPr divided by r!, because each selection of r things can be arranged in r! orders.
How large a factorial can it work out?
Every digit is worked out up to 20000! — 77,338 of them — and the Copy button carries the whole number. On screen the middle is left out once an answer runs past 10,000 digits, which first happens at 3249!. Above 20000!, and up to a billion, it gives the digit count and scientific notation instantly rather than refusing — the size of a factorial can be worked out without building the number.
Why is 0! equal to 1?
There is exactly one way to arrange nothing — the empty arrangement — and defining 0! as 1 is what makes nCr and the binomial theorem come out right at the edges. The tool follows the standard definition.
Are the results exact?
Yes, wherever the digits are shown: the arithmetic uses big integers, which have no rounding at all. The digit count and scientific notation for very large n come from a logarithm instead, and are shown as an approximation with the ≈ sign for exactly that reason.
Is anything uploaded?
No. Everything is computed in your browser with JavaScript. Nothing you type is sent anywhere or stored.