Factorial Calculator
The factorial of a non-negative integer n, denoted n!, is the product of all positive integers less than or equal to n. By convention, 0! = 1. Factorials grow extremely fast β 20! already exceeds 2.4 quintillion, and 1000! has over 2,500 digits.
This calculator uses BigInt arithmetic to compute exact factorials for values up to 1000, displaying the full result and its digit count. Factorials are fundamental in combinatorics, probability theory, and algebra, appearing in permutations, combinations, Taylor series, and many other mathematical formulas.
How it works
n! = n Γ (nβ1) Γ (nβ2) Γ ... Γ 2 Γ 1, with the special case 0! = 1. Stirling's approximation: n! β β(2Οn) Γ (n/e)^n for large n.
Use cases
- Computing permutations and combinations in probability problems
- Evaluating terms in Taylor and Maclaurin series
- Solving combinatorics problems in math competitions
- Understanding growth rates in algorithm analysis