Factorial Calculator
Calculate factorial (n!) of any positive number
Your result will appear here
What is a Factorial?
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.
n! = n × (n-1) × (n-2) × … × 3 × 2 × 1
By definition, the factorial of 0 is 1 (0! = 1). Factorials are used in mathematics, particularly in combinatorics, algebra, and mathematical analysis.
Common Factorial Examples
0! = 1
By definition
1! = 1
1 × 1
5! = 120
5 × 4 × 3 × 2 × 1
7! = 5040
7 × 6 × 5 × 4 × 3 × 2 × 1
Applications of Factorials
Factorials are widely used in:
- Combinatorics: Calculating permutations and combinations
- Probability: Determining possible outcomes in events
- Algebra: In series expansions and polynomial equations
- Calculus: In Taylor series and other mathematical expansions
This factorial calculator provides quick and accurate results for any positive integer up to 1000. For larger numbers, the result is displayed in scientific notation for better readability.