ERF.PRECISE function

Note: This draft page is under construction 🚧

Overview

ERF.PRECISE (ERror Function) is a function of the Engineering category that calculates a value for the error function. Also known as the Gauss error function, the error function represents the probability of a random variable falling within a certain range, given that it follows a specified normal distribution.

ERF.PRECISE is provided for compatibility with other spreadsheets. For all real values of $x$, $\text{ERF.PRECISE}(x)=\text{ERF}(x)$.

Usage

Syntax

ERF.PRECISE(X) => erf.precise

Argument descriptions

• X (number, required). Integration limit. ERF.PRECISE integrates over the range [0, X].

Additional guidance

None.

Returned value

ERF.PRECISE returns a number that is the error function probability for the specified argument. The returned value has a magnitude in the range [0, 1] but may be either positive (integration limit > 0) or negative (integration limit < 0).

Error conditions

• In common with many other IronCalc functions, ERF.PRECISE propagates errors that are found in its argument.

• If no argument, or more than one argument, is supplied, then ERF.PRECISE returns the #ERROR! error.

• If the value of the argument is not (or cannot be converted to) a number, then ERF.PRECISE returns the #VALUE! error.

• For some argument values, ERF.PRECISE 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 error function arises in many scientific, engineering, and mathematical fields and is commonly defined by the following equation (applicable for any real number $x$):

$$\text{erf}(x)=\frac{2}{\sqrt{\pi }}{\int }_0^x{e}^{-t^2}dt$$

• The figure below illustrates the output of the ERF.PRECISE function for values of $x$ in the range -3 to +3.

• This figure illustrates some of the key characteristics of the error function:

  • $\text{erf}(0)=0$
  • $\text{erf}(x)=-\text{erf}(x)$
  • As $x\to \mathrm{\infty }$, $\text{erf}(x)\to 1$
  • As $x\to -\mathrm{\infty }$, $\text{erf}(x)\to -1$

• The error function is a transcendental, non-algebraic mathematical function. IronCalc implements the ERF.PRECISE function by numerical approximation using a power series.

Examples

See some examples in IronCalc.

Links

• See also IronCalc's ERF, ERFC and ERFC.PRECISE functions.
• Visit Microsoft Excel's ERF.PRECISE function page.
• Both Google Sheets and LibreOffice Calc provide versions of the ERF.PROCESS function.