Factorial Calculator

What This Calculator Does

The factorial of a whole number $n$, written $n!$, just means “multiply every whole number from 1 up to $n$.” So $4! = 1 \times 2 \times 3 \times 4 = 24$.

It grows astonishingly fast - $10!$ is already over three million - and it turns up whenever you count arrangements. The number of ways to line up $n$ different things in order is exactly $n!$ (3 books fit on a shelf in $3! = 6$ different orders), which is why factorials sit at the heart of permutations and probability.

How It Works

$$n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1$$

with $0! = 1$ by definition.

Worked Examples

n	n!
0	1
1	1
5	120
7	5,040
10	3,628,800

FAQ

How do you calculate a factorial?

Multiply every whole number from 1 up to n. For 5: $5 \times 4 \times 3 \times 2 \times 1 = 120$.

Why is 0! equal to 1?

By definition — there is exactly one way to arrange zero items (the empty arrangement), so $0!$ is set to 1.

How large a factorial can this handle?

Up to 170! exactly. Factorials grow extremely fast, so larger values are not shown here.