The Excel ERF Function

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Related Functions:

ERFC

ERF.PRECISE

Error Function

The Error function is given by the equation :

Further information can be found on the Wikipedia Error Function page

Basic Description

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

The format of the function is:

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

Improvements in Excel 2010

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.

Formulas:

Examples of use of the Excel Erf Function

Results:

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.

Further examples of the Excel Erf function can be found on the Microsoft Office website.

Trouble Shooting

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

Common Errors

#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.
You will need to enable the add-in if you want to use the Excel engineering functions.

To do this in Excel 2003 :

From the Tools drop-down menu, select the option Add-Ins ...
An 'Add-Ins' window will pop up. From this, select the option Analysis ToolPak and click OK

To do this in Excel 2007 :

Click the Microsoft button on the top left of your spreadsheet and select the Excel Options button
From the menu on the left hand side, select Add-Ins
In the 'Manage:' box, select Excel Add-ins and click Go...
An 'Add-Ins' window will pop up. From this, select the option Analysis ToolPak and click OK

To do this in Excel 2010 :

Click the File tab (top left of your spreadsheet) and select Options
From the menu on the left hand side, select Add-Ins
If the window that pops up doesn't show the 'Add-ins' list, use the 'Manage:' drop-down menu (at the bottom of the window) to select Excel Add-ins. Click Go...
From the 'Add-Ins' window, select the option Analysis ToolPak and click OK

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