Back to Tools
Factorial Calculator
Sequence Master
Rapid Factorial Expansion Engine
!
About the Factorial Calculator
The factorial of a number n (written n!) is the product of all whole numbers from 1 up to n. Factorials are used for counting arrangements and in probability.
How to use the Factorial Calculator
- Enter a non-negative whole number.
- Press the calculate button to see n! and the multiplication steps.
Formula and method
n! = n × (n − 1) × (n − 2) × ... × 2 × 1, with 0! = 1.
Worked example
5! = 5 × 4 × 3 × 2 × 1 = 120. 10! = 3,628,800.
Fast growth. 5! = 120, while 10! = 3,628,800. Factorials grow so quickly that 20! already exceeds two quintillion.
When to use the Factorial Calculator
- Counting arrangements in permutation problems.
- Working with probability and combinations.
- Series expansions in calculus.
Common mistakes to avoid
- Trying to take the factorial of a negative number or a fraction with the ordinary formula.
- Forgetting that 0! equals 1.
Tips
- Factorials grow extremely quickly. 20! is already over two quintillion.
- There are n! ways to arrange n different objects in a row.
Frequently Asked Questions
By definition, which keeps formulas for permutations and combinations consistent. There is exactly one way to arrange zero items.
There is exactly one way to arrange zero items, and it keeps formulas for combinations consistent.
Very large results are shown in scientific notation because they exceed normal number limits.