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# 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.

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.