Math & Algebra Tool

Factorial Calculator

Calculate the factorial of a number.

Σ The Formula

n! = n × (n-1) × (n-2) × ... × 1

Real World Examples

Small Factorial
5! = 120 (5×4×3×2×1)
Zero Factorial
0! = 1 (by definition)
Larger Number
10! = 3,628,800
Permutation
Arranging 3 items: 3! = 6 ways

# About This Calculator

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

Factorials are fundamental in combinatorics, probability, and algebra. They help calculate the number of ways to arrange items (permutations) or choose items (combinations). For instance, the number of ways to shuffle a deck of cards is 52!, a number so huge it exceeds the atoms in the universe.

The special case is 0! = 1. This convention ensures that formulas for permutations and combinations work correctly. Factorials grow extremely fast - 10! is over 3 million, and 20! is huge.

This tool calculates the exact value of factorials for smaller numbers and helps you understand the multiplication process behind them.

How To Use

  1. Enter a non-negative integer (e.g., 5).
  2. Click Calculate.
  3. View the result and the expansion.

Frequently Asked Questions

What is 0! (zero factorial)?+

0! equals 1. This definition is crucial for mathematical formulas (like combinations) to work consistently. It represents the fact that there is exactly one way to arrange zero items (by doing nothing).

How fast do factorials grow?+

Extremely fast! 5! = 120, but 10! > 3 million, and 20! has 19 digits. This rapid growth is why they are often used in analyzing algorithm complexity.

Can I calculate factorial of a decimal or negative number?+

Standard factorial is only for non-negative integers. However, the Gamma function extends the concept to decimals and complex numbers (where Γ(n) = (n-1)!).

What are factorials used for?+

Mainly in counting, probability, and permutations (arrangements). For example, determining how many ways people can stand in a line or how many lottery number combinations exist.

Why do you stop at 1?+

Because multiplying by 0 would make the whole answer 0, which isn't useful for counting. Factorial is the product of positive integers.

Is Factorial Calculator free to use?+

Yes, Factorial Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

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