❗Factorial Calculator

About this tool

Enter a whole number from 0 to 20,000 to get the exact factorial (with a copy button), the number of digits and trailing zeros, scientific notation and Stirling's approximation. Up to 3,000 you also get the double factorial and subfactorial; decimals use the gamma function.

Factorials explained

The factorial n! is 1 × 2 × 3 × … × n, the number of ways to arrange n distinct objects. It grows faster than any exponential: 10! is 3,628,800, 20! is 2,432,902,008,176,640,000 (the largest that fits in a 64-bit integer), and 52!, the orderings of a deck of cards, has 68 digits. This tool uses arbitrary-precision integers, so results are exact rather than rounded. The number of trailing zeros is ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + …, because each zero needs a factor of 5 paired with a 2; 100! has 158 digits and 24 trailing zeros. Stirling's approximation, n! ≈ √(2πn)(n/e)^n, gets more accurate as n grows. The double factorial n!! multiplies every other number (7!! = 7 × 5 × 3 × 1 = 105), and the subfactorial !n counts derangements, arrangements where nothing is in its original place (!5 = 44). By convention 0! = 1, and the gamma function extends factorials to non-integers: 0.5! = √π/2 ≈ 0.8862. The permutation and combination calculator and the big number calculator are related.

Frequently asked questions