Special function occurring in probability, statistics, and diffusion equations.
Parameters
-3.00.0+3.0
Integral Formula
erf(x) = (2/√π) ∫₀ˣ e⁻ᵗ² dt
The Gaussian error function is the integral of the normal distribution curve.
Function Evaluation
erf(0.50)0.5205000Error Function erf(x)
Complementary erfc(x)0.4795000
High Precision (Abramowitz-Stegun)
About this calculator
Overview
The error function (also called the Gauss error function) is a special function of sigmoid shape that occurs in probability, statistics, and partial differential equations. It describes the probability of a random variable with a Normal distribution falling within a certain range.
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Pro Tips
erf(x) is an odd function: erf(-x) = -erf(x).
erfc(x) = 1 - erf(x) is the complementary error function.
The results here use high-precision numerical approximations.
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Fun Facts
"The 'Error' in the name comes from its use in measuring measurement errors."
"Directly related to the Normal Distribution: area under bell curve between -1 and 1 is erf(1/√2)."
"As x approaches infinity, erf(x) quickly approaches 1.0; it reaches 0.99 by x = 1.83!"
"Used in physics for describing heat conduction and diffusion processes."
