The ERFC function is an Engineering formula that calculates and returns the complementary error function, integrated between a lower limit and infinity. This formula essentially a subset of the error functions that calculate the probability of a value falling into a normal distribution range. This family of mathematical functions are also called Gauss error functions. In this guide, we’re going to show you how to use the ERFC function and also go over some tips and error handling methods.

Supported versions

  • All Excel versions (The function was improved in Excel 2010 to add support for negative arguments)

ERFC Function Syntax



xThe lower bound of the integral.


The ERFC function needs only a single argument as an input, x. The x value argument represents the lower bound for integrating the complementary error function. The function accepts negative numerical values in Excel versions 2010 and later. Below are some examples of its use.

=ERFC(1) integrates between 1 and ∞


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  • Other related Excel functions:
    • ERFC.PRECISE function works exactly the same as the ERFC function. ERFC.PRECISE was added for the sake of consistency between function names.
    • ERF function, can find the integration between a lower and upper limit.
    • ERF.PRECISE function returns the error function between 0 and the entered argument.
  • You can find more information about this function on Wikipedia's Error Function page.


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