# Factorial Calculator

n
factorial

Our factorial calculator is a tool that can determine the factorial of any natural number from 0 up to 170. Read on to learn what is a factorial, and what is the factorial formula. This article will also present you with rules that will make it simple for you to calculate more complex expressions involving factorials.

## What is a factorial

The easiest definition of n-factorial, denoted n!, is a product of all positive natural numbers smaller or equal to n. For example,

`6! = 6*5*4*3*2*1 = 720`

The value of 0! is by convention equal to 1.

Factorial is most often used in combinatorics, for instance when calculating the number of combinations and permutations.

## Factorial formula

We can also define a factorial in a more precise, mathematical manner:

`n! = 1` if `n = 0` and

`n! = n * (n-1)!` otherwise.

Notice that you don't have to do all the calculations to determine a factorial. For example, you already know that `6! = 720`. If you want to calculate `8!`, you can simply use the formula above:

`8! = 8 * 7! = 8 * 7 * 6! = 56 * 720 = 40 320`

`8!/5! = 8*7*6*5*4*3*2*1 / (5*4*3*2*1) = 8*7*6 = 336`

Of course, you can also use our factorial calculator and spare yourself some time. Just enter the number in the box above. The result is presented using scientific notation. If you decide to keep this notation, remember about using a correct number of significant figures.

## Basic values of factorials

• 0! = 1
• 1! = 1
• 2! = 2
• 3! = 6
• 4! = 24
• 5! = 120
• 6! = 720
• 7! = 5040
• 8! = 40 320
• 9! = 362 880
• 10! = 3 628 800

For factorials of numbers greater than 10, don't hesitate to use the factorial calculator above.

## Factorials of non-integer values

It is possible to determine the factorial of non-integer numbers - basically, for all real numbers excluding negative integers. It requires the use of complex mathematical tools, such as mathematical analysis. Still, we can tell you that `(-0.5)! = √π` and `(0.5)! = 0.5√π`.

`(2.5)! = 2.5 * (1.5)! = 2.5 * 1.5 * (0.5)! = 1.875√π`