How to use the Factorial Calculator
Enter a whole number n from 0 upwards. The calculator multiplies every whole number from 1 to n and shows the exact result.
Worked examples
5! is 5 × 4 × 3 × 2 × 1 = 120, which is the number of ways to line up five people. 10! is already 3,628,800. By the time you reach 52!, the number of ways to shuffle a deck of cards, the result has 68 digits, which is why exact arithmetic matters here.
Why 0! equals 1
There is exactly one way to arrange nothing, so 0! is defined as 1. It also keeps formulas consistent: n! equals n × (n − 1)!, and setting n to 1 only works if 0! is 1. Factorials are only defined for whole numbers that are zero or greater.
The formula
n! = n × (n − 1) × … × 1
Examples
- 10!
10! = 3,628,800 Digits: 7
- 5!
5! = 120 Digits: 3
- 20!
20! = 2,432,902,008,176,640,000 Digits: 19
Limitations and assumptions
Exact integer arithmetic.
Frequently asked questions
What is 0 factorial?
0! is defined as 1.
Why do factorials grow so fast?
Each step multiplies by a larger number, so 10! is 3,628,800 and 20! is over 2.4 quintillion.
What is a factorial used for?
Counting arrangements: 5 people can sit in a row in 5! = 120 ways.
Can I take the factorial of a negative number?
No, factorials are defined for non-negative integers.