n
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How this calculator works
The factorial of n, written n!, is the product of every whole number from 1 to n. It counts the ways to arrange n different items in a row. Factorials grow extremely fast: 20! already has 19 digits and 100! has 158. Results here are exact, not rounded.
Formula
- n! = n × (n − 1) × … × 2 × 1
- 0! = 1
- Number of arrangements of n items = n!
Worked example
10!
- n
- 10
Result10! = 3,628,800
The product of the whole numbers from 1 to 10 has 7 digits.
Frequently asked questions
Why is 0 factorial equal to 1?
There is exactly one way to arrange zero items: do nothing. Defining 0! = 1 also keeps formulas such as n! = n × (n − 1)! consistent.
What is a factorial used for?
Counting permutations and combinations, in probability, and in series such as the Taylor expansion of eˣ.
Can you take the factorial of a negative or fractional number?
Not with this definition. The gamma function extends factorials to non-integers, with Γ(n + 1) = n!.
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Results are estimates based on the values you enter and the published method shown above. They do not replace professional medical, financial or legal advice. Method reviewed October 7, 2026. About this site