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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 erfc(x)=1erf(x). Also known as the complementary Gauss error function, the complementary error function represents the probability of a random variable falling outside a certain range, given that it follows a specified normal distribution.

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 x):
erfc(x)=2πxet2dt
  • The figure below illustrates the output of the ERFC function for values of x in the range -3 to +3.
  • This figure illustrates some of the key characteristics of the complementary error function:

    • erfc(0)=1
    • erfc(x)=2erfc(x)
    • As x, erfc(x)0
    • As x, erfc(x)2
  • 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.