Error function Calculator

What is the error function?

In applied mathematics, we come across the error function, commonly referred to as the Gaussian error function and frequently abbreviated as erf. In addition to being used in applied mathematics to solve differential equations and in physics to solve the heat equation when the Heaviside step function determines the boundary conditions, the inverse error function is also used in statistics to calculate critical values, p-values, and confidence intervals, all of which are related to statistical hypothesis testing and estimation.

The error function is a non-elementary particular function in mathematics that appears in probability, statistics, and partial differential equations. Another name for it is the probability integral.

The error function is defined as:

\( erf(x) = \dfrac{2}{π} \int_0^x  exp(-t^2) \,dt\)

Any number on the real line can have its error function calculated using the erf calculator. Along with a function plot displaying where erf(x) falls about other potential function values, the output also includes the complementary error function for the same number. For any real value of x, erf(x) provides a result between zero and one.

Inverse Error Function

The output of the inverse error function mode includes both the erf’s inverse and complement. A real value between minus one and one must be provided as (y ∈ [-1, 1]).

How to Use the Error Function Calculator?

The error function calculator should be used as follows:

1. Enter a real number in the box.
2. To perform the calculation, click “CALCULATE”.
3. The provided real number x’s the error function calculator will calculate errors function.

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