# Stirling Formula

The Stirling formula or Stirling’s approximation formula is used to give the approximate value for a factorial function (n!). This can also be used for Gamma function. Stirling’s formula is also used in applied mathematics. It makes finding out the factorial of larger numbers easy. Let’s see how we use this formula for the factorial value of larger numbers.

## Formula of Stirling’s Approximation

The Stirling formula for “n” numbers is given below:

 n! ≈ √2π nn + ½ e−n

Also Check: Factorial Formula

### Solved Examples Using Stirling’s Formula

Question: What will be the factorial of 11 using Stirling’s formula?

Solution:

Using the formula: n! ≈ √2π nn+½ e−n

11! ≈ √2π 1111+ e−11

= 39615625.05