Factorial Calculator
Calculate the factorial (n!) of any positive integer. Fast, free, and fully client-side.
Calculator Inputs
Number (n)
Factorial Result—
How the Factorial Calculator Works
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. Factorials are ubiquitous in probability, permutations, combinations, and mathematical series expansions.
Formula
n! = n × (n - 1) × (n - 2) × ... × 2 × 1 (with 0! = 1)
Recursive definition: n! = n × (n - 1)! for all integers n > 0.
Calculation Example
5! = 5 × 4 × 3 × 2 × 1 = 120.
Frequently Asked Questions
Why is 0 factorial equal to 1?
By definition in combinatorics, there is exactly one way to arrange zero objects (the empty set), making 0! = 1.
How fast do factorials grow?
Factorials grow faster than exponential functions; for instance, 10! = 3,628,800 and 20! is over 2.4 quintillion.