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Gamma Function via Stirling Approximation Calculator

Approximate Γ(n) and n! for large non-integer values.

Approximates the gamma function Γ(z) using Stirling's series for z > 0: Γ(z) ≈ √(2π/z) · (z/e)^z. For integer z, Γ(n) = (n−1)!. Returns ln(Γ) for large z to avoid overflow.

Marcus Laurent By Marcus Laurent
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

Γ(z) ≈ √(2π/z)·(z/e)^z

In depth

Approximates the gamma function Γ(z) using Stirling's series for z > 0: Γ(z) ≈ √(2π/z) · (z/e)^z. For integer z, Γ(n) = (n−1)!. Returns ln(Γ) for large z to avoid overflow.