# gamma() Function & Examples

Use the gamma() probability function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

## gamma

#### gamma(n)

Try it yourself:

```calculio
gamma(4)
3!
gamma(1/2)
sqrt(pi)
```

[factorial](https://calcul.io/function/factorial/index.md)

---

## Extend factorials with gamma

**gamma(n)** evaluates the gamma function, which satisfies `gamma(n) = (n - 1)!` for positive integers. It extends factorial-style calculations to non-integer and complex values.

## Examples

`gamma(6)` is 120, and gamma values also exist for positive fractional inputs. This makes gamma useful in continuous probability distributions and special-function formulas. Use [factorial](https://calcul.io/function/factorial/index.md) for ordinary non-negative integer counts and [lgamma](https://calcul.io/function/lgamma/index.md) for a logarithmic representation.

## Domain caveats

Gamma has poles at zero and negative integers, so those inputs are undefined. Values can grow rapidly, and floating-point evaluation may lose precision near poles. [round](https://calcul.io/function/round/index.md) is useful for display but should not hide a near-singular input. For binomial-style quantities, [combinations](https://calcul.io/function/combinations/index.md) is normally the clearer function.

[All functions](https://calcul.io/functions/index.md)