Error Function calculator estimates the value of error function for the given a real number $x$ by using the integration formula. It is an online probability and statistics tool for data analysis programmed to estimate the relative precision of the approximation.
It is necessary to follow the next steps:
The error function, or sometimes called the Gauss error function is a special function of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion. The error function is denoted by $\mbox{erf}(x)$ and it is determined by the following formula
The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing data to understand the theory of probability and statistics. In many applications, it is necessary to calculate precision approximation, where this error function calculator can assist us to make calculation easy. In physics, the error function is used in Maxwell-Boltzmann distributions because the velocities of particles are normally distributed. The integrals of velocity distributions, give error functions and are important in various stability criteria for plasmas in thermal equilibrium.
Practice Problem 1:
Find $\mbox{erf}(5)$.
Practice Problem 2:
Evaluate integral $\frac{2}{\sqrt{\pi}}\int_5^{10}e^{-x^2}dx$.
The error function calculator, formula and practice problems would be very useful
for grade school students (K-12 education) to understand the concept of the error function. This concept can be of benefit in the solutions of diffusion problems in heat, mass and momentum transfer, probability theory, the theory of errors, etc.