Python math Module

The math module in Python provides a wide range of mathematical functions and constants that are highly useful for performing mathematical operations. It supports operations like trigonometry, logarithms, square roots, and constants such as pi and Euler’s number. This module is essential for applications involving complex mathematical calculations and algorithms.

This guide will introduce you to the most commonly used functions and constants in the math module.

1. Importing the math Module

To use the math module in your Python program, you need to import it first.

import math

2. Constants in the Math Module

The math module includes several constants that can be useful in mathematical computations.

• math.pi: The mathematical constant π (approximately 3.14159).
• math.e: The base of natural logarithms, Euler’s number (approximately 2.71828).
• math.inf: Represents positive infinity.
• math.nan: Represents a “Not-a-Number” value.

Example: Using Constants

import math

print("Pi:", math.pi)
print("Euler's number:", math.e)
print("Infinity:", math.inf)
print("Not-a-Number:", math.nan)

3. Basic Mathematical Functions

math.sqrt(x)

This function returns the square root of a number x.

import math

result = math.sqrt(16)
print(result)  # Outputs: 4.0

math.pow(x, y)

This function returns x raised to the power of y.

result = math.pow(2, 3)
print(result)  # Outputs: 8.0

math.fabs(x)

This function returns the absolute value of x.

result = math.fabs(-5)
print(result)  # Outputs: 5.0

math.ceil(x)

This function returns the smallest integer greater than or equal to x (ceiling of x).

result = math.ceil(4.2)
print(result)  # Outputs: 5

math.floor(x)

This function returns the largest integer less than or equal to x (floor of x).

result = math.floor(4.8)
print(result)  # Outputs: 4

4. Trigonometric Functions

math.sin(x), math.cos(x), math.tan(x)

These functions return the sine, cosine, and tangent of x (in radians).

import math

angle = math.radians(30)  # Convert degrees to radians
print("sin(30°):", math.sin(angle))  # Outputs: 0.49999999999999994
print("cos(30°):", math.cos(angle))  # Outputs: 0.8660254037844387
print("tan(30°):", math.tan(angle))  # Outputs: 0.5773502691896257

math.radians(x)

This function converts an angle from degrees to radians.

result = math.radians(30)
print(result)  # Outputs: 0.5235987755982988

math.degrees(x)

This function converts an angle from radians to degrees.

result = math.degrees(math.pi / 6)
print(result)  # Outputs: 30.0

5. Logarithmic Functions

math.log(x, base)

This function returns the logarithm of x to the specified base. If the base is not provided, the natural logarithm (base e) is returned.

import math

result = math.log(8, 2)
print(result)  # Outputs: 3.0 (since 2^3 = 8)

math.log10(x)

This function returns the base-10 logarithm of x.

result = math.log10(100)
print(result)  # Outputs: 2.0

math.log2(x)

This function returns the base-2 logarithm of x.

result = math.log2(32)
print(result)  # Outputs: 5.0

6. Factorial and Combinatorics

math.factorial(x)

This function returns the factorial of a number x, which is the product of all integers from 1 to x.

result = math.factorial(5)
print(result)  # Outputs: 120 (5! = 5 * 4 * 3 * 2 * 1)

math.comb(n, k)

This function returns the number of ways to choose k items from n items without regard to the order (combinations).

result = math.comb(5, 2)
print(result)  # Outputs: 10 (5 choose 2)

math.perm(n, k)

This function returns the number of ways to choose k items from n items with regard to the order (permutations).

result = math.perm(5, 2)
print(result)  # Outputs: 20 (5 permute 2)

7. Special Functions

math.gcd(x, y)

This function returns the greatest common divisor (GCD) of x and y.

result = math.gcd(48, 180)
print(result)  # Outputs: 12

math.isqrt(x)

This function returns the integer square root of x (the greatest integer less than or equal to the square root of x).

result = math.isqrt(16)
print(result)  # Outputs: 4

8. Hyperbolic Functions

math.sinh(x), math.cosh(x), math.tanh(x)

These functions return the hyperbolic sine, cosine, and tangent of x.

import math

x = 1
print("sinh(1):", math.sinh(x))  # Outputs: 1.1752011936438014
print("cosh(1):", math.cosh(x))  # Outputs: 1.5430806348152437
print("tanh(1):", math.tanh(x))  # Outputs: 0.7615941559557649

Conclusion

The math module in Python provides a rich set of mathematical functions and constants that simplify a wide range of calculations, from basic arithmetic to more advanced topics such as trigonometry, logarithms, and combinatorics. Whether you’re solving equations, performing statistical analysis, or working with scientific data, the math module will be an essential tool for your Python programming toolkit.