Stirling's formula

Stirling showed that with the constant k = e the sequence (xn) with xn = n!kn/nn converges to √(2π).

This means that for large n we have the approximation n! ≈ √(2πn) (n/e)n.

nn!Stirling's approximation
103.629 × 1063.604 × 106
1009.333 × 101579.425 × 10157
10004.024 × 1025764.464 × 102576