ERF Function

Basic Description

The Excel ERF function calculates the Error Function, integrated between two supplied limits.

Syntax: ERF( lower_limit, [upper_limit] )

where the arguments are as follows:

lower_limit The lower limit of the integral

(or if no [upper limit] is supplied, the integral of the Error function between 0 and the supplied lower_limit is returned)

[upper_limit] An optional argument which, if supplied, gives the upper limit of the integral

If the [upper_limit] argument is omitted, the integral of the error function between 0 and the supplied lower_limit is returned

The Erf function has been improved in Excel 2010 in that it can now accept negative function arguments. In Excel 2007 or earlier, if you input a negative value for the upper or lower limit, the function would return an error. However, in Excel 2010, the function algorithm has been improved, so that it can now calculate the function for both positive and negative ranges.

 

Erf Function Examples

The spreadsheet on the right shows examples of the Excel Erf function being used to calculate the integral of the Error Function between different limits. The functions are shown in the top spreadsheet and the results are shown in the bottom spreadsheet. Note that the functions in cells A1 and A2 are both performing the same calculation – ie. the integral between 0 and 1.5.

 Formulas:

Examples of use of the Excel Erf Function

 Results:

Excel Erf Function Results

Erf Function Common Errors

If you get an error from the Excel Erf function this is likely to be one of the following :

#NUM! In Excel 2007 or earlier: Occurs if either of the supplied arguments are negative
#VALUE! Occurs if any of the supplied arguments are non-numeric
#NAME? Occurs when Analysis ToolPak add-in is not enabled in your Excel.

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