Factorial Calculator
The factorial of n, written n!, is the product of every whole number from 1 up to n. It counts how many ways you can arrange n items and is the building block of permutations and combinations.
Your numbers
Result
- Number of digits
- 3
| Step | Detail |
|---|---|
| 5! | 5 x 4 x 3 x 2 x 1 |
| Result | 120 |
| Number of digits | 3 |
How factorials work
n! multiplies all whole numbers from 1 to n: 5! = 5 x 4 x 3 x 2 x 1 = 120. By definition 0! = 1 (there is exactly one way to arrange nothing). Factorials grow extremely fast — 10! is already over 3.6 million, and 20! passes 2 quintillion.
Where factorials appear
Factorials count arrangements. The number of ways to order n distinct items is n!. They power permutations and combinations, and appear throughout probability, algebra (the binomial theorem) and calculus (Taylor series).
Frequently asked questions
Sources
- Factorial (product of integers from 1 to n)
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