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# 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.

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.