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Factorial Calculator

Enter a Number (n)

Result

120

👤

Reviewed by Dr. Alex M., Ph.D.

Last updated: November 2025

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💡 Expert Tips

Why is 0! = 1?

This is defined this way because it makes mathematical formulas work. The number of ways to arrange 0 items is 1 (do nothing). It's also necessary for the binomial theorem and other formulas to work correctly.

Factorials Grow FAST

Factorials increase incredibly quickly. 10! = 3,628,800. 20! = 2,432,902,008,176,640,000. By 70!, you're already past the number of atoms in the universe!

Real-World Use: Permutations

If you have 5 books, there are 5! = 120 different ways to arrange them on a shelf. In general, n items can be arranged in n! ways.

⚠️ Common Mistakes

Thinking 0! = 0

The most common error. Remember: 0! = 1, not 0. It's a special definition that makes math work cleanly.

Confusing with Exponents

5! ≠ 5^5. Factorial means 5×4×3×2×1 = 120. Exponent means 5×5×5×5×5 = 3,125. Very different!

Negative Numbers

Factorials are only defined for non-negative integers. (-5)! is undefined.

❓ Frequently Asked Questions

What is a factorial? +

A factorial of a non-negative integer n, written as n!, is the product of all positive integers less than or equal to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

What is 0 factorial? +

0! = 1 by definition. This might seem counterintuitive, but it's defined this way to make many mathematical formulas work consistently, especially in combinatorics and calculus.

How do you calculate a factorial? +

To calculate n!, multiply all positive integers from 1 to n. For example: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720. For 0!, the result is 1 by definition.

What is the largest factorial I can calculate? +

In JavaScript (which this calculator uses), factorials greater than 170! result in Infinity because the number exceeds the maximum value JavaScript can represent.

Can you calculate factorial of negative numbers? +

No, factorials are only defined for non-negative integers (0, 1, 2, 3, ...).