Factorial Calculator
Compute n! — the factorial of any whole number — with exact big-integer precision, even for very large n. Free, instant and private: everything runs in your browser.
Results appear instantly up to n = 3,000. Larger values (up to 100,000) are computed exactly when you press Calculate — very large n can take a few seconds.
How to use the factorial calculator
- Enter a whole number. Type any integer from 0 to 100,000 into the box, or click one of the example buttons like 52! (the number of ways to shuffle a deck of cards).
- Press Calculate n!. Small values are computed as you type; big ones are computed exactly the moment you press the button.
- Copy or download the result. You get every digit of the exact answer, plus the digit count, trailing zeros and a scientific-notation approximation.
About this tool
The factorial of n, written n!, is the product of all positive integers from 1 up to n — so 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow explosively: 20! already exceeds the capacity of a 64-bit integer, and 100! has 158 digits. This factorial calculator uses arbitrary-precision (big-integer) arithmetic with a fast divide-and-conquer product, so it returns the exact value — not a rounded approximation — for any n up to 100,000, a number with 456,574 digits. Factorials appear everywhere in mathematics: counting permutations and combinations, probability, binomial coefficients and Taylor series.
All calculations run locally in your browser using JavaScript's native BigInt support. Nothing you type is sent to a server, the tool is free with no limits, and you can copy the full result to the clipboard or download it as a plain-text file for use in other programs. For related counting problems, try the combinations and permutations calculator.
Frequently asked questions
Why does 0! equal 1?
By convention 0! = 1 because it is an empty product — multiplying no numbers at all leaves the multiplicative identity, 1. This convention also makes the formulas for permutations and combinations work: there is exactly one way to arrange zero objects.
Can I calculate the factorial of a negative or decimal number?
No — the ordinary factorial is only defined for non-negative whole numbers. The Gamma function Γ(x) extends factorials to decimals and complex numbers (with n! = Γ(n + 1)), but this tool focuses on exact integer factorials.
How large a factorial can this tool compute?
Up to n = 100,000, whose factorial has 456,574 digits. The result is exact to the last digit thanks to big-integer arithmetic; only the fixed cap keeps the computation fast in a browser tab.
What do the trailing zeros mean?
Trailing zeros are the zeros at the end of n!. Each one comes from a factor of 10 = 2 × 5, and since factors of 5 are scarcer than factors of 2, the count equals ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + … — a classic result used in math competitions.