Why is 0! equal to 1?

0! is defined as 1 because there is exactly one way to arrange an empty set of zero objects, and to maintain consistency with the combinatorics formula n! = n × (n-1)!.

What is Stirling's approximation?

Stirling's approximation is a mathematical formula used to estimate factorials of very large numbers: n! ≈ √(2πn) * (n/e)ⁿ.

Can you compute factorials of decimal values?

Traditional factorials apply only to non-negative integers. Decimals are computed using the Gamma Function: Γ(x) = (x-1)!.

Math Tool✨ New Release

Factorial Calculator

Calculate the factorial of any non-negative integer (n!). Supports exact integer factorials, scientific notation for larger numbers, and Stirling's approximation.

Interactive Factorial Calculator Workspace

Live Solver

Integer n (for n!)

Factorial Result

5! = 120

Factorial Series Calculation

Multiply numbers sequentially: 5 × 4 × 3 × 2 × 1

Mathematical Formula & Variables

Equation Modeln! = n × (n - 1) × (n - 2) × ... × 1 | 0! = 1

A factorial is the product of all positive integers less than or equal to n. The gamma function extends this to non-integers.

Variable Definitions

Symbol	Description
n	A non-negative integer
n!	The calculated factorial product

How to Use the Factorial Calculator

Type a non-negative integer n into the numeric input field.
Click calculate to output the factorial value.
View the complete multiplication series breakdown and scientific representations for large inputs.