Gamma Function Calculator

Gamma Function Calculator

Evaluate the gamma function Γ(n), which extends factorials beyond whole numbers.

Last updated: June 2026 | By Patchworkr Team

Gamma Evaluation
Gamma extends factorials: for positive integers n, Γ(n) = (n - 1)!.
Result
Value
Γ(5)
24
Γ(5) = 4!

What gamma means

The gamma function generalizes factorials to a wider domain and is defined everywhere except at non-positive integers.

Validation

Inputs must be finite numbers. Non-finite values and poles are rejected explicitly.

Formula and example

Γ(n + 1) = nΓ(n)

Example: Γ(4) = 3! = 6.

Worked Example

Evaluate Γ(4).

1. Use the factorial relation: Γ(4) = 3!.

2. Compute 3! = 3 x 2 x 1.

3. The result is 6.

Final answer: 6

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