Factorial Calculator

A factorial is the product of an integer and every smaller positive integer. This product is represented by the symbol n!, which is called n factorial. By convention, 0! = 1. Thus,

0! = 1

2! = (2)(1) = 2

3! = (3)(2)(1) = 6

4! = (4)(3)(2)(1) = 24

5! = (5)(4)(3)(2)(1) = 120

and so on ...

Factorials can get very big, very fast. The term 10,000! is the largest factorial that the Factorial Calculator can evaluate. The term 10,000! is equal to about 2.846 x 10³⁵⁶⁵⁹.

For an example that computes a factorial, see Sample Problem 1.

The Factorial Calculator uses Scientific notation to express very large numbers. Scientific notation is a way to write numbers that are too large or too small to be concisely written in a decimal format.

With scientific notation, any positive integer can be expressed as a number between 1 and 10 multiplied by a power of 10. Here is an example of a number written using scientific notation:

3.02 * 10¹² = 3,020,000,000,000

The Factorial Calculator uses E notation to express very large numbers. E notation is a way to write numbers that are too large or too small to be concisely written in a decimal format.

With E notation, the letter E represents "times ten raised to the power of". Here is an example of a number written using E notation:

3.02E12 = 3.02 * 10¹² = 3,020,000,000,000

The Factorial Calculator displays results in three formats: scientific notation, E notation, and ordinary integers.

The integer results are exact for all computations up to 10,000 factorial (10,000!). Results reported in scientific notation and E notation are also exact up to 21 factorial (21!). Beyond 21 factorial, results reported in scientific notation and in E notation are very good approximations, accurate to 14 significant digits.

The Factorial Calculator can compute a factorial for any number up to 10,000.

Beyond 10,000, the calculator reports a lower-bound estimate. Here's the logic. The value of 10,000! is approximately 2.846 x 10³⁵⁶⁵⁹. Therefore, we know the factorial of any integer greater than 10,000 will be at least 10³⁵⁶⁶³. So, for any integer bigger than 10,000, the calculator reports that the factorial value will be more than 10³⁵⁶⁶³.