The ERF function is an Engineering formula that calculates and returns the error function, integrated between specified lower and upper limits. In this guide, we’re going to show you how to use the ERF function, and also go over some tips and error handling methods.

Supported versions

  • All Excel versions (The function was improved in Excel 2010 to include support for negative numbers.)

ERF Function Syntax

ERF(lower_limit, [upper_limit])


lower_limit The lower bound of the integration.
[upper_limit] Optional. The upper bound of the integral. If omitted, ERF returns the integration between 0 and the lower_limit.


Lower limit only

The lower_limit is the only required argument for the ERF function. If you want to calculate the integral between 0 and a numeric value. You only need to enter a lower_limit value The ERF function accepts negative numerical values in Excel 2010 and newer versions. Below is an example set,

=ERF(1) integrates between 0 and 1

erf function

Lower Limit and Upper Limit

Enter an [upper_limit] argument to set both lower and upper limits to be used in the error function. The [upper_limit] argument is very similar to the lower_limit as it accepts numerical values without a sign (in Excel 2010 and later). Here is how you can use the ERF function with both arguments:

=ERF(1,2) integrates between 1 and 2

If you look at the screenshots, you can see ERF(1) and ERF(0,1) returns same value.

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  • Other related Excel functions:
    • ERF.PRECISE returns the error function between 0 and the entered argument.
    • ERFC and ERFC.PRECISE functions return complementary error function integrated between x and infinity. (Both functions work similarly. The ERFC.PRECISE function was added to provide consistency between function names.)
  • You can find further details on Wikipedia's Error Function page.


  • If the lower_limit is non-numeric, the ERF returns the #VALUE! error value.
  • If the [upper_limit] is non-numeric, the ERF returns the #VALUE! error value.
  • The ERF function returns the #NUM! error value if one or both of the arguments are negative in Excel 2007 or earlier versions.