$Factorial$

Factorial

Calculate the factorial n! and double factorial n!! exactly, with all digits, up to n = 1000. Number of digits, trailing zeros, Stirling formula.

What to find:

Factorial n!

Double factorial n!!

n is a whole number from 0 to 1000. The result is exact, without rounding.

Test yourself

The factorial calculator computes n! and the double factorial n!! exactly — all digits, without rounding, for n up to 1000. It also shows the number of digits, the trailing zeros and Stirling's approximation.

What is a factorial

n! = 1 · 2 · 3 · … · n, 0! = 1

n	0	1	2	3	4	5	6	7	8	10
n!	1	1	2	6	24	120	720	5040	40320	3628800

The factorial grows very fast: 20! ≈ 2.4 · 10¹⁸, and 100! has 158 digits.

Useful properties

n! = n · (n − 1)! — handy for simplifying: 10!/8! = 10 · 9 = 90.
Trailing zeros of n! (Legendre's formula): [n/5] + [n/25] + [n/125] + … For 100!: 20 + 4 = 24 zeros.
Stirling's formula: n! ≈ √(2πn) · (n/e)ⁿ.
Double factorial: n!! = n · (n − 2) · (n − 4) · …, for example 9!! = 9 · 7 · 5 · 3 · 1 = 945.

The factorial is the basis of combinatorics: n! is the number of permutations of n objects, and arrangements and combinations are expressed through factorials.