Factorial Calculator
Free factorial calculator. Find the factorial of any positive integer instantly. Includes explanation of factorials and permutations.
Free Tool
No Sign-up
Instant Results
Factorial Calculator
Comprehensive Guide & Practice
Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.
1
1. What Is a Factorial?
The factorial of a non-negative integer n, written n!, is the product of all positive integers from 1 to n. Formula: n! = n × (n−1) × (n−2) × ... × 2 × 1
Examples: 5! = 5 × 4 × 3 × 2 × 1 = 120. 10! = 3,628,800. By definition, 0! = 1.
2
2. Where Are Factorials Used?
- Permutations: The number of ways to arrange n items in order = n! Ways to arrange 5 books on a shelf = 5! = 120.
- Combinations: nCr = n! ÷ (r! × (n−r)!). Ways to choose 3 items from 5 = 10.
- Probability: Factorials appear in binomial distributions and many probability formulas.
- Taylor Series: Factorials appear in infinite series expansions of functions like eˣ and sin(x).
See also: Combination & Permutation Calculator | Probability Calculator | Probability Basics