Factorial Calculator
Enter a whole number to calculate its factorial — the product of every whole number from 1 up to that number, a fundamental building block for combinations, permutations, and probability.
n!
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Enter a number to calculate.
How the Factorial formula works
The factorial definition:
n! = n × (n−1) × (n−2) × ... × 2 × 1 0! = 1 (by definition)
Step-by-step calculation
- Start with the number itself.
- Multiply by every whole number below it, down to 1.
- The final product is the factorial.
Worked example
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
Frequently asked questions
Why is 0! defined as 1, not 0?
It's a mathematical convention that keeps formulas involving factorials (like combinations and permutations) consistent — treating 0! as an 'empty product' equal to 1 makes those formulas work correctly at their boundary cases.
How fast do factorials grow?
Extremely fast — 10! is already 3,628,800, and 20! exceeds 2.4 quintillion. Factorials grow faster than exponential functions, which is why they quickly exceed what standard number formats can precisely represent.