# Error Function Erf(x) Calculator

 An easy to use calculator to compute the error function $$\text{Erf} \; (x)$$ defined by the integral $\displaystyle \text{Erf} \; (x) = \dfrac{2}{\sqrt{\pi}} \int_0^{x} \; e^{-t^2} \; dt$ is presented.
The $$\text{Erf} \; (x)$$ function has many applications
The graph of the error function $$\text{Erf} \; (x)$$ is shown below and indicates that it is an odd function. The relationship between the cumulative distribution function (CDF) $$F_{X} (x)$$ of the standard normal distribution of the continuous variavle $$X$$ given by
$\displaystyle F_{X} (x) = \dfrac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} \; e^{- \frac{1}{2} t^2} \; dt$
and the error function is given by
$F_{X} (x) = \dfrac{1}{2} \left(1 + \text{Erf}( x / \sqrt{2}) \right)$
It is shown that the relationship between the error function Erf(x) and the cumulative normal distribution $$F_{X} (x)$$ with a mean $$\mu$$ and a standard deviation $$\sigma$$, is given by $F_{X} (x) (x,\mu,\sigma) = \dfrac{1}{2} \left(1 + \text{Erf} \left( \dfrac{x-\mu}{ \sqrt{2} \sigma} \right) \right)$

## Use of The Erf Calculator

Enter the argument $$x$$ as a real number and the number of decimal places desired, and click calculate.

 $$\quad x =$$ 3 Decimal Places Desired = 10