What This Calculator Does
The Factorial Calculator finds the factorial of a non-negative whole number, written as n!. Factorials are used throughout mathematics and statistics, especially in counting problems like permutations and combinations, where they describe the number of ways a set of items can be arranged.
The Formula
The factorial of a number n is the product of every positive integer from 1 up to n: n! = n x (n-1) x (n-2) x … x 2 x 1. By definition, 0! equals 1. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Why Factorials Grow So Fast
Factorials increase extremely quickly. 10! is already 3,628,800, and 20! is over 2.4 quintillion. Because of this rapid growth, this calculator supports values of n up to 170, beyond which the result exceeds what standard double-precision numbers can represent accurately.
- 0! and 1! both equal 1 by mathematical definition
- Factorials are only defined for non-negative integers
- Commonly used in probability, statistics, and combinatorics for general educational purposes