Error Function Calculator
Calculate the error function (erf) and complementary error function (erfc) for any real number.
Calculate Error Function
Table of Contents
What is Error Function?
The error function (erf) is a special function that appears in probability, statistics, and partial differential equations. It is defined as the integral of the Gaussian function and is related to the normal distribution.
- Integral of Gaussian function
- Related to normal distribution
- Used in probability theory
- Important in statistics
Properties
Symmetry
erf(-x) = -erf(x)
Limits
erf(0) = 0, erf(∞) = 1
Complementary
erfc(x) = 1 - erf(x)
Range
-1 ≤ erf(x) ≤ 1
Error Function Formula
The error function is defined by the following integral:
Where:
- x is the input value
- π is pi (approximately 3.14159)
- e is Euler's number (approximately 2.71828)
Applications
Probability Normal Distribution
Used to calculate probabilities in normal distribution and to find confidence intervals.
Physics Heat Transfer
Used in solving heat conduction problems and diffusion equations.
Engineering Signal Processing
Used in digital signal processing and communication theory.