Factorial Calculator

Step 1: Enter a non-negative integer (0, 1, 2, ..., up to 1000).

Step 2: Click Calculate.

Step 3: See the factorial value, scientific notation, and step-by-step expansion. Very large factorials are computed with arbitrary-precision integers.

The factorial of a non-negative integer n, written n!, is the product of all positive integers from 1 up to n. For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.

By definition, 0! = 1 and 1! = 1. This might seem odd, but it is the convention that makes the rules of combinatorics work consistently — it's the 'empty product' (a product with no factors is 1, just as an empty sum is 0).

Factorials grow extraordinarily fast. 10! is about 3.6 million. 20! is over 2 quintillion. 100! has 158 digits. By n = 170, factorials exceed what can be represented in standard floating-point numbers — this calculator uses JavaScript BigInt for exact results beyond that point.

n! = 1 × 2 × 3 × ... × n

Recursive definition: n! = n × (n−1)!

Special cases: 0! = 1 and 1! = 1

Example: 5! = 5 × 4 × 3 × 2 × 1 = 120

Related formulas:
• Permutations: nPr = n! / (n−r)!
• Combinations: nCr = n! / (r! × (n−r)!)

Example 1: 5! = 1 × 2 × 3 × 4 × 5 = 120 — the number of ways to arrange 5 books on a shelf.

Example 2: 10! = 3,628,800 — possible orders for 10 runners in a race.

Example 3: 52! ≈ 8.07 × 10⁶⁷ — the number of possible orderings of a standard deck of cards (more than the number of atoms in the observable galaxy).

0! = 1 by convention — this makes combinatorics formulas work.

Factorials explode fast. 20! already exceeds 2 quintillion.

52! is astronomically large — a well-shuffled deck has never been in that exact order before.

Permutations and combinations both use factorials.