Factorial Calculator
Compute n! for whole numbers, with exact results for large values.
What the Factorial Calculator does
The factorial of n is the product of every whole number from 1 to n. It counts the number of ways to arrange n distinct items, which makes it the backbone of permutations and combinations.
Formula
n! = n × (n−1) × (n−2) × … × 2 × 10! = 1 by definition
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| n | number | Yes | Accepts 0 or more, up to 2000. |
How to use it
- Enter n.
- Select Calculate.
Worked example
How many ways can 5 books be arranged on a shelf?
- n
- 5
5! = 5 × 4 × 3 × 2 × 1 = 120 arrangements.
Frequently asked questions
Why is 0! equal to 1?
There is exactly one way to arrange nothing — the empty arrangement. Defining 0! as 1 also keeps the combination formula consistent.
Can I take the factorial of a decimal?
Not with this calculator. Fractional factorials require the gamma function, where n! = Γ(n+1).