The Excel ERFC Function

Complementary Error Function

The Complementary Error Function is equal to 1 - ERF (i.e. 1 - Error Function), and is given by the equation:

Complementary Error Function Equation
For further information, see the Wikipedia Error Function page
Related Functions:
ERF
ERFC.PRECISE

Basic Description

The Excel ERFC function calculates the Complementary Error Function, integrated between a supplied lower limit and infinity.

The syntax of the function is:

ERFC( x )

where x is the lower limit of the integral.

Improvements in Excel 2010

The Erfc function was 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 argument, x, 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 values of x.

Erfc Function Examples

In the following spreadsheet, the Excel Erfc function is used to calculate the Complementary Error Function integral for three different lower limits.

 Formulas:
 AB
1=ERFC( 0 ) - integral between 0 and ∞
2=ERFC( 0.5 ) - integral between 0.5 and ∞
3=ERFC( -1 ) - integral between -1 and ∞
 Results:
 AB
11 - integral between 0 and ∞
20.479500122 - integral between 0.5 and ∞
31.842700793 - integral between -1 and ∞

Further examples of the Excel Erfc function are provided on the Microsoft Office website.


Erfc Function Errors

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

Common Errors
#NUM!-Occurs in older versions of Excel (Excel 2007 or earlier), if the supplied value of x is negative.
#VALUE!-Occurs if the supplied value of x is non-numeric.