0! = 1 is defined by convention and is consistent with combinatorics: there is exactly 1 way to arrange zero objects. It also makes the formula n! = n × (n-1)! work for n=1.

Where are factorials used?

Factorials appear in permutations (arrangements), combinations (selections), probability distributions (binomial, Poisson), Taylor series expansions, and the definition of the Gamma function.

21! exceeds the maximum safe integer in JavaScript (2⁵³ - 1 ≈ 9 × 10¹⁵). Values above 20! would lose precision. For larger factorials, use logarithms or arbitrary-precision libraries.

Factorial Calculator — n!

The Factorial Calculator computes n! (n factorial) — the product of all positive integers from 1 to n. Factorials grow astronomically fast and are fundamental in combinatorics, probability, statistics, and calculus. For example, 10! = 3,628,800 and 20! = 2,432,902,008,176,640,000.

n (non-negative integer)

Frequently Asked Questions

n! (n factorial) = n × (n-1) × (n-2) × ... × 2 × 1. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By convention, 0! = 1.

Related Calculators

🧮Permutation Calculator 🧮Combination Calculator 🧮Probability Calculator