Factorial Calculator

About this calculator

The factorial of a whole number n, written n!, is the product of every positive integer from 1 up to n (0! is defined as 1 by convention), so 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow extremely fast — 10! is already over 3.6 million, and 170! is roughly the largest factorial a standard double-precision number can represent before overflowing.

Factorials are the building block of combinatorics: they’re used directly in the formulas for permutations, nPr = n! ÷ (n − r)!, and combinations, nCr = n! ÷ (r! × (n − r)!), which in turn underpin probability calculations for things like card hands, lottery odds, and password or combination-lock possibilities. Students meet factorials early in algebra and statistics courses, and they also appear in calculus in Taylor series expansions.

This calculator takes a whole number from 0 to 170 and returns its factorial.