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Python math.erfc() Method

The Python math.erfc() method is used to calculate the complementary error method, which is defined as 1 − erf(x), where erf(x) is the error method.

This method represents the probability of an event lying outside a certain range for a normally distributed random variable. Mathematically, the complementary error method is defined as −

$$\mathrm{erfc(x)\:=\:1\:-\:erf(x)\:=\frac{2}{\sqrt{\prod}}\int_{x}^{∞}\:e^{-t^{2}}dt}$$

Where, e is the base of the natural logarithm and π is the mathematical constant pi. The complementary error method is an even method, meaning that erfc(-x) = erfc(x) and is being bounded between 0 and 2.

Following is the basic syntax of the Python math.erfc() method −

math.erfc(x)

This method accepts a real number or a numeric expression as a parameter for which you want to calculate the complementary error method.

The method returns the value of the complementary error method evaluated at x.

In the following example, we are calculating the complementary error method for a positive real number using the math.erfc() method −

import math
x = 1.5
result = math.erfc(x)
print("Complementary Error method for x =", x, ":", result)

The output obtained is as follows −

Complementary Error method for x = 1.5 : 0.033894853524689274

In here, we are calculating the complementary error method for a negative real number using the math.erfc() method −

import math
x = -0.75
result = math.erfc(x)
print("Complementary Error method for x =", x, ":", result)

Following is the output of the above code −

Complementary Error method for x = -0.75 : 1.7111556336535152

In this example, we are evaluating the sum of complementary error methods for x=2 and x/2 using the math.erfc() method −

import math
x = 2
result = math.erfc(x) + math.erfc(x/2)
print("Complementary Error method expression result for x =", x, ":", result) 

We get the output as shown below −

Complementary Error method expression result for x = 2 : 0.1619769420313324

Now, we use the math.erfc() method to directly calculate the complementary error method for x=0 −

import math
x = 0
result = math.erfc(x)
print("Complementary Error method for x =", x, ":", result)

The result produced is as shown below −

Complementary Error method for x = 0 : 1.0

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