Introduction to Error Function Calculator
Error function calculator is an online statistic tool that is used to calculate the error of given functions in a normal distribution system and let you know what is erf in math.
Our erfc calculator can compute various types of error function table problems like error function value, inverse error function, complementary error function, and inverse complementary error function and give solutions to these complex problems in less than a minute.
What is an Error Function?
Error function method is the abbreviation of erf that is used in statistics or probability to find the error of the given function with the help of the integration process.
It is also known as the Gauss error function method. An error function in statistics is an odd function whose limits are from -1 to 1 for both negative x value and positive x value respectively.
Formula Used by Erf Calculator
Error function formula is defined in terms of the integration process where x is the limit value. The error function table formulas used by the error function calculator to solve the error function problems are,
Error Function Formula
$$ y \;=\; erf\; x \;=\; \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt \; \; \; \; \; for \; x \ge 0, \; y [0,1] $$
Where,
$$ t \;=\; \frac{x}{\sqrt{2} \sigma} $$
Inverse Error Function:
The inverse error function formula is defined as,
$$ erf( erf^{-1}(x)) \;=\; x $$
Complementary Error Function
The complementary error function formula is defined as,
$$ erfc(x) \;=\; 1 - erf(x) $$
Inverse Complementary Error Function:
The inverse complementary error function formula is defined as,
$$ erfc^{-1}(x) \;=\; erf^{-1}(1-x) $$
- Erf x is the Gauss error function value
- t refers to time in a normal distribution
- x is the complex number in the distribution
- e-t2 is an exponential function of time
Stepwise Evaluation Process of Erfc Calculator:
Error function calculator evaluates the different types of error in the normal distribution system with the help of the formula of error function in a simple and easy method so that you can understand this concept very well.
Although error function problems have a complex procedure sometimes but our Erf calculator can manage these types of error complexity and provide you the solution in a few seconds.
When you enter the input function value in the erf function calculator, it analyzes the behavior of the function first. After analyzing it add all the input values in the given formula of the error function to find its solution.
Erf(x) calculator can use a different method to solve the heat equation problem for finding errors like the Taylor series, Macluin series, geometric, or sometimes powers series also, it all depends on the nature of the input function.
As you can see in the below example where derivation are involved in the input value and to solve this type of question fundamental theorem of calculus is used. In the same way, you can give various types of error functions and it will provide you exact solution as per your given function value.
How to Calculate ERF - An Example
An example of an error function is given to let you know about the manual calculation of such problems so you may be able to understand the results of the Error function calculator and can solve it by yourself as well.
Example:
The error function formula is,
$$ erf(x) \;=\; \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt $$
So, using this calculate the following,
$$ \frac{d}{dx} \biggr[ erf(\sqrt{x}) \biggr] $$
Solution:
$$ erf(\sqrt{x}) \;=\; \frac{2}{\sqrt{\pi}} \int_0^{\sqrt{x}} e^{-t^2} dt $$
Differentiating,
$$ \frac{d}{dx} \biggr(erf( \sqrt{x}) \biggr) \;=\; \frac{2}{\sqrt{\pi }} \int_0^{\sqrt{x}} e^{-t^2} dt $$
Using the second fundamental theorem of calculus,
$$ \frac{d}{dx} \biggr(erf( \sqrt{x}) \biggr) \;=\; \frac{2}{\sqrt{\pi }} \biggr((e^{-(\sqrt{x})^2}) \frac{d}{dx} \sqrt{x} - e^{-0^2} \frac{d}{dx}0 \biggr) $$
$$ \;=\; \frac{2}{\sqrt{\pi }} \biggr( e^{-x} \frac{1}{\sqrt[2]{x}} - 0 \biggr) $$
$$ \;=\; \frac{2}{\pi } \biggr( \frac{e^{-x}}{2 \sqrt{x}} \biggr) $$
$$ \;=\; \frac{e^{-x}}{\sqrt{\pi x}} $$
So,
$$ \frac{d}{dx}(erf(\sqrt{x})) \;=\; \frac{e^{-x}}{\sqrt{\pi x}} $$
How to Use the Error Function Calculator?
Erf function calculator has a user-friendly interface that enables everyone to easily use this calculator to solve error function problems.
You should follow our instructions before using this erf calculator so that you can avoid getting into any trouble during the evaluation. These instructions are:
- Choose the type of error from the given list (error function, inverse error function, complementary error, or inverse complementary error) of erf(x) calculator.
- Enter the error function in erfc calculator’s input field.
- Add the decimal number in your answer
- Review your input function (error function) before hitting the calculate button.
- Click on the “Calculate” button to get the solution of the error function in a probability distribution.
- Press the “Recalculate” button that brings you back to a new page for the calculation of more distribution error functions
Result from the Erf Function Calculator:
You will get the result of the error function as per your given error function from the error function calculator in a few seconds. It may include as
- Result box
It provides the solution to your given error function problems
- Possible steps option
Steps option gives you a solution for various types of errors in step by step method when you click on steps options.
- Plot option
Plot option sketch as per the given value of the error function so that you get a visual understanding.
Benefits of Using Erf(x) Calculator
Erf calculator provides you with a ton of benefits while you are using it to calculate the error value function in a normal distribution system. You just need to enter your function and you will get the result in no time. These benefits are:
- It is a trustworthy tool as it always provides accurate results of error value functions with less or no mankind mistakes in calculation and you would understand how to calculate erf.
- Our erfc calculator is a speedy tool that provides solutions for different kinds of function errors in a fraction of a second.
- It does not demand you to pay any charges for a premium subscription because it is a free online tool that gives you solutions without any fee.
- You should use our erf function calculator for the practice of error function table questions so that you get a strong hold on the gradient of this statistic concept.
- Error function calculator has a simple design that can be accessible to everyone even a beginner who can use it easily.
