Factorial Calculator
Calculate the factorial of any non-negative integer. The factorial of n (written as n!) is the product of all positive integers from 1 to n. Used extensively in combinatorics, probability, and mathematical analysis. Supports calculations for large numbers.
Calculate Factorial
Quick Examples
0!
1
1!
1
5!
120
10!
3,628,800
15!
1.3 trillion
20!
2.4 quintillion
50!
3.04 x 10^64
100!
9.33 x 10^157
About Factorial
The factorial of a non-negative integer n, denoted n!, is the product of all positive integers less than or equal to n.
n! = n x (n-1) x (n-2) x ... x 2 x 1
By convention, 0! = 1.
Factorials grow extremely fast. For example, 20! already exceeds 2 quintillion.
FAQ
What is a factorial?
A factorial (n!) is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120. By definition, 0! = 1.
What are factorials used for?
Factorials are essential in combinatorics for calculating permutations and combinations. They appear in probability theory, Taylor series, and many areas of mathematics and computer science.
How fast do factorials grow?
Factorials grow extremely fast - faster than exponential functions. 10! = 3,628,800. 20! = 2.4 quintillion. 100! has 158 digits. This rapid growth is important in algorithm complexity analysis.