Factorial Calculator - Free Online n! Math Tool

Using the Factorial Solver

Enter a non-negative integer in the input field.
The factorial is calculated instantly and displayed in full.
For large n, the result scrolls - copy it for use in combinatorics or probability.
The result shows the digit count as a convenient indicator of magnitude.

Factorial Calculator is a high-precision math tool that computes the product of all positive integers from 1 up to n. Written as n!, the factorial of 5 is 5 × 4 × 3 × 2 × 1 = 120. Factorials grow extremely rapidly - 20! is 2,432,902,008,176,640,000 (18 digits) and 100! has 158 digits. This tool uses JavaScript BigInt to compute exact results without floating-point overflow, handling inputs up to several hundred.

Combinatorics and n! Calculations

Factorials are the foundation of combinatorics. The number of ways to arrange n distinct items is n! (permutations). Combinations (choosing r items from n without order) use C(n,r) = n! / (r! × (n−r)!). Factorials appear in Taylor series expansions, the Gamma function, Stirling's approximation, and in probability distributions like the Poisson and binomial. This compute factorial tool is essential for anyone dealing with permutations and combinations.

Exact integer result using JavaScript BigInt - no floating-point approximation
Shows digit count for large results
Handles inputs up to 1,000 (results have thousands of digits)
Step-by-step multiplication breakdown for small n (≤ 10)

Frequently Asked Questions

What is 0! (zero factorial)?

By definition, 0! = 1. This is not a convention - it follows from the combinatorial interpretation: there is exactly one way to arrange zero objects (doing nothing).

How fast does factorial grow?

Extremely fast. 10! = 3,628,800. 20! ≈ 2.4 × 10¹⁸. 100! ≈ 9.3 × 10¹⁵⁷. 1000! has 2,568 digits. Factorial growth is much faster than exponential growth.

What is Stirling's approximation?

For large n, n! ≈ √(2πn) × (n/e)ⁿ. This provides a closed-form approximation that is accurate to within 1% for n ≥ 10 and becomes more accurate as n grows. Useful when you only need the order of magnitude.

Is there a factorial for non-integers?

Yes - the Gamma function extends factorial to all complex numbers except negative integers: Γ(n) = (n−1)!. So Γ(1.5) = 0.5! ≈ 0.886. This appears in statistics (the Gamma distribution) and physics.

For related math tasks, try our GCD/LCM Calculator, Fraction Calculator, or the Average Calculator. Bookmark this page whenever you need a reliable Factorial Calculator.

Factorial Calculator online

Calculate n! - exact result for large numbers using BigInt