Stirling's Formula

The Stirling's Formula Factorial calculator estimates the factorial function for larger numbers.

INSTRUCTIONS: Enter the following:

• (n) Positive Integer

Stirling's Factorial Estimate (n!): The calculator returns the estimate rounded to the nearest integer.

The Math / Science

Stirling's Formula, approximates n!.  This can be useful for large values of n.  As n grows, the approximation's difference from truth approaches zero.
The equation for Stirling's Formula is:

     `n!  ≈  sqrt(2*pi) * e^(-n) * n^(n+ 1/2)`

Combinatorics Calculators

• n! - factorial
• `n!  sqrt(2 pi n) (n/e)^n` - Stirling's factorial approximation
• _nC_k - combinations
• C_r(n,k) - combinations with repetitions
• _nP_k - permutations
• P_r(n) - permutations with repetitions
• P_comp(n,2) - Comparison permutations
• P_c(n,r) - Circular Permutation