# A to Z of Excel Functions: the ERF Function

27 December 2018

*Welcome back to our regular A to Z of Excel Functions blog. Today we look at the ERF function. *

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**The ERF function**

In mathematics, the error function (also called the Gauss error function or ERF) is a special, non-elementary function that occurs in probability, statistics and partial differential equations describing diffusion. It is defined as:

In statistics, for nonnegative values of **x**, the error function has the following interpretation: for a random variable **Y** that is normally distributed with mean 0 and variance 1/2, **ERF(x)** describes the probability of **Y** falling in the range [**−x**,** x**].

This function returns the error function integrated between **lower_limit** and **upper_limit**.

The **ERF **function employs the following syntax to operate:

**ERF(lower_limit, [upper_limit])**

The **ERF** function has the following arguments:

**lower_limit:**this is required and represents the lower bound for integrating**ERF****upper_limit:**this argument is optional. This represents the upper bound for integrating**ERF**. If omitted,**ERF**integrates between zero and**lower_limit**.

It should be further noted that:

- if
**lower_limit**is nonnumeric,**ERF**returns the*#VALUE!*error value - if
**upper_limit**is nonnumeric,**ERF**returns the*#VALUE!*error value.

Please see my example below:

*We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every business day.*

*A full page of the function articles can be found here. *