Factorial Calculator
The factorial n! multiplies all integers from 1 to n. Useful in probability and combinatorics.
Calculator
Use the Factorial Calculator
Result
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Formula
n! = n × (n−1) × … × 1
Step-by-step
- 1
Enter n
Any integer 0 or more.
- 2
Read the result
Note: 0! is defined as 1.
Worked example
Example input: n: 5
Result: 120
Related tools
- Permutation Calculator
Uses factorials.
- Combination Calculator
Uses factorials.
Frequently asked questions
What is 5 factorial?
120 — 5! = 5 × 4 × 3 × 2 × 1. Factorials count arrangements: 5 different books line up in exactly 120 different orders. Enter 5 above and the calculator multiplies the chain for you. A sixth book would push the count to 720 arrangements.
Why is 0 factorial equal to 1?
By definition, backed by logic: there is exactly one way to arrange zero items — the empty arrangement. It also keeps the pattern consistent, since 1! = 1 × 0! forces 0! = 1.
How quickly do factorials grow?
Very fast: 10! is already 3,628,800, 20! tops 2.4 × 10¹⁸, and 52! — the ways to shuffle a card deck — beats the seconds since the Big Bang. That growth is why arrangement counting needs small sets.