n! Factorial Calculator (n!)

Factorial Result

What is a Factorial?

The factorial of a non-negative integer n, written as n!, is the product of all positive integers from 1 to n. Factorials are widely used in permutations, combinations, and probability.

n! = n Ɨ (nāˆ’1) Ɨ (nāˆ’2) Ɨ ... Ɨ 2 Ɨ 1
5! = 5 Ɨ 4 Ɨ 3 Ɨ 2 Ɨ 1 = 120

Factorial Table

0!
1 (by definition)
5!
120
10!
3,628,800
12!
479,001,600

Frequently Asked Questions

What is 0 factorial? ā–¼
0! = 1. This is defined by convention and is essential for combinatorics formulas to work correctly when n = r.
What is 10 factorial? ā–¼
10! = 10 Ɨ 9 Ɨ 8 Ɨ 7 Ɨ 6 Ɨ 5 Ɨ 4 Ɨ 3 Ɨ 2 Ɨ 1 = 3,628,800.
Why are factorials used in combinations? ā–¼
Factorials count the number of ways to arrange items. C(n,r) = n! / (r! Ɨ (nāˆ’r)!) uses factorials to count selections without regard to order.