You may encounter a special `ValueError`

when working with Python’s `math`

module.

ValueError: math domain error

Python raises this error when you try to do something that is not mathematically possible or mathematically defined.

To understand this error, have a look at the definition of the **domain**:

“*The domain of a function is the complete set of possible values of the independent variable. Roughly speaking, the domain is the set of all possible (input) x-values which result in a valid (output) y-value.*” (source)

The domain of a function is the set of all possible input values. If Python throws the `ValueError: math domain error`

, you’ve passed an undefined input into the `math`

function. Fix the error by passing a valid input for which the function is able to calculate a numerical output.

Here are a few examples:

## Python Math Domain Error Sqrt

The math domain error appears if you pass a negative argument into the `math.sqrt()`

function. It’s mathematically impossible to calculate the square root of a negative number without using complex numbers. Python doesn’t get that and throws a `ValueError: math domain error`

.

Here’s a minimal example:

from math import sqrt print(sqrt(-1)) ''' Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 2, in <module> print(sqrt(-1)) ValueError: math domain error '''

You can fix the math domain error by using the `cmath`

package that allows the creation of complex numbers:

from cmath import sqrt print(sqrt(-1)) # 1j

## Python Math Domain Error Log

The `math domain error`

for the `math.log()`

function appears if you pass a zero value into it—the logarithm is not defined for value 0.

Here’s the code on an input value outside the domain of the logarithm function:

from math import log print(log(0))

The output is the math domain error:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module> print(log(0)) ValueError: math domain error

You can fix this error by passing a valid input value into the `math.log()`

function:

from math import log print(log(0.000001)) # -13.815510557964274

This error can sometimes appear if you pass a very small number into it—Python’s float type cannot express all numbers. To pass a value “close to 0”, use the `Decimal`

module with higher precision, or pass a very small input argument such as:

math.log(sys.float_info.min)

## Python Math Domain Error Acos

The `math domain error`

for the `math.acos()`

function appears if you pass a value into it for which it is not defined—arccos is only defined for values between -1 and 1.

Here’s the wrong code:

import math print(math.acos(2))

The output is the math domain error:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module> print(math.acos(2)) ValueError: math domain error

You can fix this error by passing a valid input value between [-1,1] into the `math.acos()`

function:

import math print(math.acos(0.5)) # 1.0471975511965979

## Python Math Domain Error Asin

The `math domain error`

for the `math.asin()`

function appears if you pass a value into it for which it is not defined—arcsin is only defined for values between -1 and 1.

Here’s the erroneous code:

import math print(math.asin(2))

The output is the math domain error:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module> print(math.asin(2)) ValueError: math domain error

You can fix this error by passing a valid input value between [-1,1] into the `math.asin()`

function:

import math print(math.asin(0.5)) # 0.5235987755982989

## Python Math Domain Error Pow

The `math domain error`

for the `math.pow(a,b)`

function to calculate a**b appears if you pass a negative base value into it and try to calculate a negative power of it. The reason it is not defined is that any negative number to the power of 0.5 would be the square number—and thus, a complex number. But complex numbers are not defined by default in Python!

import math print(math.pow(-2, 0.5))

The output is the math domain error:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module> print(math.pow(-2, 0.5)) ValueError: math domain error

If you need a complex number, a^{b} must be rewritten into e^{b ln a}. For example:

import cmath print(cmath.exp(0.5 * cmath.log(-2))) # (8.659560562354932e-17+1.414213562373095j)

You see, it’s a complex number!

## NumPy Math Domain Error — np.log(x)

import numpy as np import matplotlib.pyplot as plt # Plotting y = log(x) fig, ax = plt.subplots() ax.set(xlim=(-5, 20), ylim=(-4, 4), title='log(x)', ylabel='y', xlabel='x') x = np.linspace(-10, 20, num=1000) y = np.log(x) plt.plot(x, y)

This is the graph of `log(x)`

. Don’t worry if you don’t understand the code, what’s more important is the following point. You can see that log(x) tends to negative infinity as x tends to 0. Thus, it is mathematically meaningless to calculate the log of a negative number. If you try to do so, Python raises a math domain error.

>>> math.log(-10) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: math domain error

## Where to Go From Here?

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To help students reach higher levels of Python success, he founded the programming education website Finxter.com. He’s author of the popular programming book Python One-Liners (NoStarch 2020), coauthor of the Coffee Break Python series of self-published books, computer science enthusiast, freelancer, and owner of one of the top 10 largest Python blogs worldwide.

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