Factorial Calculator
Calculate the factorial of a number (n!). Factorial is the product of all positive integers from 1 to n. Used in permutations, combinations, and probability. Supports integers up to 170.
Factorial calculator
Factorial (n!)
What is this?
Factorial (n!) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By convention, 0! = 1. Used in permutations, combinations, and probability. Factorials grow very fast: 10! is over 3 million, and 20! is over 2 quintillion. The calculator supports integers up to 170 to avoid overflow; beyond that, the numbers exceed standard floating-point precision. Factorials appear in the binomial coefficient formula and many counting problems.
When to use
Use for permutations (arrangements), combinations (selections), probability, or combinatorics. Example: How many ways to arrange 5 books? 5! = 120. C(10,3) = 10!/(3!×7!) = 120. Students solve combinatorics problems. Programmers verify recursive or iterative factorial implementations. Statisticians use factorials in probability distributions. Anyone counting arrangements or selections needs factorials. The calculator handles the large numbers so you do not have to.
How to use
n! = n × (n−1) × (n−2) × … × 1. Enter a non-negative integer. Max 170 to avoid overflow.
0! = 1 by definition
Frequently asked questions
- Factorial (n!) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
- By convention, 0! is defined as 1. This makes formulas for permutations and combinations work correctly when n = 0.