Factorial Calculator

Enter a non-negative integer to compute its factorial (n!). The factorial of n is the product of all positive integers less than or equal to n.

What is a Factorial?

The factorial of a non-negative integer n, denoted n!, is the product of all positive integers from 1 to n:

n! = n × (n-1) × (n-2) × ... × 2 × 1

By convention, 0! = 1. This is known as the empty product — the product of no numbers is defined as the multiplicative identity.

Common Factorial Values

Applications of Factorials

• Permutations — The number of ways to arrange n distinct objects is n!
• Combinations — C(n, k) = n! / (k! × (n-k)!) counts the ways to choose k items from n
• Probability — Factorials appear in binomial, Poisson, and other distributions
• Taylor Series — Functions like e^x and sin(x) use factorials in their series expansions