ERFC function
Note: This draft page is under construction 🚧
Overview
ERFC (ERror Function Complementary) is a function of the Engineering category that calculates a value for the complementary error function, defined by
Usage
Syntax
ERFC(X) => erfc
Argument descriptions
- X (number, required). The lower integration limit to be used to calculate the complementary error function. ERFC integrates over the range [X,
).
Additional guidance
None.
Returned value
ERFC returns a number that is the complementary error function probability for the specified argument. The returned value lies in range [0, 2].
Error conditions
In common with many other IronCalc functions, ERFC propagates errors that are found in its argument.
If no argument, or more than one argument, is supplied, then ERFC returns the
#ERROR!
error.If the value of any argument is not (or cannot be converted to) a number, then ERFC returns the
#VALUE!
error.For some argument values, ERFC may return the
#DIV/0!
error.For more information about the different types of errors that you may encounter when using IronCalc functions, visit our Error Types page.
Details
- The complementary error function arises in many scientific, engineering, and mathematical fields and is commonly defined by the following equation (applicable for any real number
):
- The figure below illustrates the output of the ERFC function for values of
in the range -3 to +3.
This figure illustrates some of the key characteristics of the complementary error function:
- As
, - As
,
The complementary error function is a transcendental, non-algebraic mathematical function. IronCalc implements the ERFC function by numerical approximation using a power series.
Examples
See some examples in IronCalc.
Links
- See also IronCalc's ERF, ERF.PRECISE and ERFC.PRECISE functions.
- Visit Microsoft Excel's ERFC function page.
- Both Google Sheets and LibreOffice Calc provide versions of the ERFC function.