# erf() Function & Examples

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

## erf

#### erf(x)

Try it yourself:

```calculio
erf(0.2)
erf(-0.5)
erf(4)
```

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## erf(): The Gaussian Error Function

**erf()** calculates the error function, a smooth function closely connected to the normal distribution and diffusion processes. It integrates a Gaussian curve, so it appears in probability, heat flow, signal analysis, and statistics.

## Interpreting values

For real input, erf(x) lies between −1 and 1, is odd, and approaches those limits as magnitude grows. erf(0) is zero. It relates a standard normal cumulative probability to an input scaled by √2, which makes it useful when translating between Gaussian models and probability statements.

Use [exp()](https://calcul.io/function/exp/index.md) in explicit Gaussian formulas, [sqrt()](https://calcul.io/function/sqrt/index.md) for standard-deviation scaling, and [abs()](https://calcul.io/function/abs/index.md) for symmetric error magnitudes. For a tail probability, avoid subtracting nearly equal values when precision matters; choose a numerically suitable formulation.

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