# A to Z of Excel Functions: The ERFC Function

3 January 2019

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

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**The ERFC 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**].

The complementary error function, denoted by **ERFC(x)**, is defined as

This function returns the complementary **ERF** function integrated between **x** and infinity.

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

**ERFC(x)**

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

**x:**this is required and represents the lower bound for integrating**ERFC**.

It should be further noted that:

- If
**x**is nonnumeric,**ERFC**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.