Factorial Calculator
Enter a non-negative integer to compute its factorial — the product of all positive integers from 1 up to that number.
Factorial Calculator
Compute n! — n factorial
n! = n × (n−1) × (n−2) × … × 2 × 1. By definition, 0! = 1.
What Is a Factorial?
n! (read 'n factorial') is the product of all positive integers from 1 up to n:
n! = n × (n−1) × (n−2) × … × 3 × 2 × 1
By definition, 0! = 1.
**Fast growth**: Factorials grow extremely quickly. 10! = 3,628,800 and 70! is already larger than a googol (10¹⁰⁰). This calculator handles factorials up to n = 100.
**Uses**: Counting permutations (n! ways to arrange n items), combinations, probability, series expansions (Taylor series), and combinatorics.
- n! = n × (n−1) × … × 1
- 0! = 1 by definition
- Grows extremely fast
- Used in permutations and combinations
Worked Example
Example: 5!
5! = 5 × 4 × 3 × 2 × 1 = 120
Example: 0!
0! = 1 (by definition)
Example: 10!
10! = 3,628,800
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Open calculator →Frequently Asked Questions
Why is 0! = 1?
It's defined that way so that combinatorics formulas (like combinations) work consistently. It also represents 'one way to arrange zero items' — do nothing.
Can factorials be negative?
No. Factorials are defined for non-negative integers only. (The gamma function extends the idea to non-integers, but that's a different tool.)
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