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:

Table of Contents

## 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?

Enough theory. Let’s get some practice!

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While working as a researcher in distributed systems, Dr. Christian Mayer found his love for teaching computer science students.

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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