Factorial Calculator
Calculate the factorial (n!) of a whole number — the product of all positive integers up to n.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter a whole number to calculate its factorial (n!) — the product of all positive integers up to that number.
A whole number from 0 to 500.
Your result
3628800
n!
Number of digits in the result7
AI explanation
Formula
n! = n × (n−1) × (n−2) × ... × 2 × 1, with 0! defined as 1Worked example
10!
| Field | Value |
|---|---|
| Number (n) | 10 |
| n! | 3628800 |
| Number of digits in the result | 7 |
Assumptions
- Factorial grows extremely fast — 100! already has 158 digits. This calculator computes the exact value up to n = 500.
Frequently asked questions
What is a factorial?
The factorial of a whole number n (written n!) is the product of all positive integers from 1 up to n. For example, 4! = 4 × 3 × 2 × 1 = 24.
Why is 0! equal to 1?
By mathematical convention, 0! is defined as 1 — this makes formulas involving factorials (like permutations and combinations) work correctly at the boundary case of zero items.
What is factorial used for?
Factorials are fundamental to combinatorics — counting permutations and combinations — as well as probability, series expansions, and algorithm analysis. See the Permutation and Combination calculators for direct applications.