Factorial Calculator

By convention, 0! = 1. This is defined to make combination and permutation formulas work correctly when n = 0. It is also consistent with the recursive definition n! = n × (n-1)!: if 1! = 1, then 0! = 1!/1 = 1.

Factorials appear in permutations (number of ways to arrange n items = n!) and combinations (n choose k = n! / (k!(n-k)!)). For example, the number of ways to arrange 5 books on a shelf is 5! = 120. The number of possible 5-card poker hands uses combination formulas.

Factorials grow faster than exponential functions. 170! ≈ 7.26 × 10³⁰⁶ is near the maximum value a standard floating-point number can represent. Beyond 170!, the result exceeds the range of standard double precision numbers, requiring arbitrary-precision arithmetic libraries.