The Python Math Module

Getting Started

Previously, we covered the Python operators that add flexibility to expressions in our code. However, the language extends further and gives us a wide range of mathematical capabilities through its built-in math module, based on the C standard library.

To get started with the module, we can import it into our Python environment, like so:

import math

Note: For complex numbers, Python has a cmath module.

Python Constants

First off, the math module has some crucial mathematical constants, including Pi, Euler's constant, as well as others. They can improve the consistency of our code bases and help us shy away from hard-coding these values.

import math

print(math.pi) # Output: 3.141592653589793

print(math.e)  # Output: 2.718281828459045

By default, Python displays the first 15 digits, and always returns a floating-point value.

For instance, we can use this approach instead of hardcoding py, to calculate the area of a circle with a given radius:

import math

radius = 7

circumference = 2 * round(math.pi, 2) * radius

print("The circumference of a circle with radius", radius, "is", circumference)

# Output: The circumference of a circle with a radius of 7 is 43.96

As you may have noticed, our code calculates the circumference of a circle with a radius of 7, using rounded Pi with 2 decimal places.

Aside from these two, the module includes other mathematical constants, such as Tau (the ratio of a circle's circumference to its radius), inf (infinity), and NaN (representing not-a-number).

Arithmetic Functions

Let's highlight some basic mathematical operations, such as finding the floor, ceiling, and factorial of a number to showcase how these module functions can simplify our workflow and conveniently perform common arithmetic.

For instance, the math.floor() function returns the closest integer value that is less than or equal to the number we input. In contrast to math.ceil(), which rounds up, math.floor() rounds down, and they both return an integer.

import math

result = math.floor(4.7)

print("The floor of 4.7 is", result) 

# Output: The floor of 4.7 is 4

import math

result = math.ceil(4.7)

print("The ceiling of 4.7 is", result)

# Output: The ceiling of 4.7 is 5

Additionally, we can find the factorial of a number with the math.factorial() function. Bear in mind, that the only accepted argument is a positive integer, and if we provide a negative value we'll get an error from the interpreter as a result.

import math

result = math.factorial(5)

print("The factorial of 5 is", result)

# Output: The factorial of 5 is 120

import math

result = math.factorial(-7)

# Output: ValueError: factorial() not defined for negative values

Power Functions in Python

With the math module, we have math.pow() and math.exp() at our disposal to tackle aspects such as calculating the power of a number, or finding its natural exponent.

Note: The math.pow() function returns a floating-point value of a number raised to a specified power in the second argument it takes.

import math

result = math.pow(7, 2)

print("2 raised to the power of 3 is", result) 

# Output: 2 raised to the power of 3 is 49.0

print(type(result)) # Output: <class 'float'>

On the other hand, with math.exp(), we calculate the exponential value of a number also returning a floating-point value.

import math

result = math.exp(7)

print("The exponential value of 1 is", result)
# Output: The exponential value of 1 is 1096.6331584284585

Greatest Common Divisor in Python

Another interesting and neat function from the module is the math.gcd() function, returning the greatest common divisor of two numbers.

import math

result = math.gcd(12, 8)

print("The greatest common divisor of 12 and 8 is", result)

# Output: The greatest common divisor of 12 and 8 is 4

The math Module Extended

To avoid information fatigue, we briefly covered some concepts so to spike interest in experimentation. Python's math module has a wealth of other capabilities such as logarithmic, trigonometric, hyperbolic, and angular conversion functions.

If you want to find out more about their nature and implementation, we encourage you to refer to the official Python documentation and go over the comprehensive table provided below.

Useful Resources

The Basics of Numbers in Python

Operators in Python