What does the ! button mean?
The factorial symbol is written after a number: n!. For a positive integer n, multiply every positive integer from n down to 1.
Why 5! equals 120
Start at 5 and multiply downward: 5 × 4 = 20; 20 × 3 = 60; 60 × 2 = 120; 120 × 1 = 120. Therefore, 5! = 120.
Common factorial values
| Expression | Result |
|---|---|
| 0! | 1 |
| 1! | 1 |
| 2! | 2 |
| 3! | 6 |
| 4! | 24 |
| 5! | 120 |
| 6! | 720 |
| 10! | 3,628,800 |
Why 0! equals 1
By the standard mathematical definition, 0! = 1. This convention keeps factorial formulas consistent in combinations, permutations and other areas of mathematics.
How to use factorial on OfficeCalculator.Net
Switch the main calculator to Scientific mode and use the n! function. The current implementation accepts non-negative integers up to 170 so the result stays within the supported finite number range.
Where factorial is used
Factorials appear in permutations, combinations, probability, series and combinatorics. If you need arrangements or selections rather than just n!, use the Permutation Calculator or Combination Calculator.
Frequently asked questions
What is 5 factorial?
5 factorial is 120.
What does ! mean after a number?
It is the factorial operator when used in this mathematical context.
Can I take factorial of a negative number on a basic calculator?
The ordinary factorial function for basic calculators is defined for non-negative integers; extensions such as the gamma function are a separate topic.
What is 0 factorial?
0! is defined as 1.
Open the matching OfficeCalculator.Net tool and test the examples with your own values.