Python offers powerful tools for performing mathematical operations—ranging from simple arithmetic to advanced functions like trigonometry and logarithms. Whether you're working on data analysis, game development, or scientific computing, this guide will help you navigate the essential math functions in Python.

Why Use Math Functions?

Python's math functions allow you to:

  • Perform precise calculations.
  • Handle floating-point numbers with care.
  • Work with constants like π and e.
  • Simplify complex equations with built-in methods.

They come in two flavors:

  1. Built-in functions – always available.
  2. math module functions – import the math module to access them.

📌 Built-in Math Functions

Function Description
abs(x) Absolute value
round(x, n) Round to n decimal places
pow(x, y) x to the power of y
max(x, y, ...) Largest value
min(x, y, ...) Smallest value
sum(iterable) Sum of elements

math Module Functions (import math)

To unlock more mathematical power, use Python’s math module:

import math

Note:

The following are the most-used functions only, checkout the complete list on docs.python.org.

🔢 Number Theory & Rounding

Function Description
math.ceil(x) Round up
math.floor(x) Round down
math.trunc(x) Truncate fractional part
math.isqrt(x) Integer square root
math.factorial(x) x!
math.fmod(x, y) Modulo with floats
math.remainder(x, y) IEEE remainder
math.copysign(x, y) x with the sign of y

📐 Trigonometry

Function Description
math.sin(x) Sine (x in radians)
math.cos(x) Cosine
math.tan(x) Tangent
math.asin(x) Inverse sine
math.acos(x) Inverse cosine
math.atan(x) Inverse tangent
math.atan2(y, x) Arctangent of y/x
math.hypot(x, y, ...) Euclidean norm √(x² + y² + …)
math.degrees(x) Convert radians to degrees
math.radians(x) Convert degrees to radians

📊 Exponentials & Logarithms

Function Description
math.exp(x) e ** x
math.expm1(x) e ** x - 1 (more accurate for small x)
math.log(x, base) Logarithm (default base e)
math.log2(x) Base-2 logarithm
math.log10(x) Base-10 logarithm
math.pow(x, y) x to the power y (float version)

🧬 Special Functions

Function Description
math.gamma(x) Gamma function
math.lgamma(x) Log(abs(gamma(x)))
math.erf(x) Error function
math.erfc(x) Complementary error function

📏 Floating Point & Precision

Function Description
math.fabs(x) Absolute float value
math.isclose(a, b) Are a and b close?
math.dist(p, q) Distance between points
math.nextafter(x, y) Smallest float > x toward y
math.ulp(x) Unit in the last place

🔍 Finite/Infinite/NaN Checks

Function Description
math.isfinite(x) Is finite?
math.isinf(x) Is infinite?
math.isnan(x) Is NaN?

🧮 Constants

Constant Description
math.pi π ≈ 3.14159
math.e Euler's number ≈ 2.71828
math.tau τ = 2π ≈ 6.28318
math.inf Infinity
math.nan Not a number

⚙️ Practical Example

Here’s a real-world demo that uses almost every function listed above:
You can run it and see the output online here: pythononline.net/#ka0YkL

import math

# Built-in functions
print("abs(-7):", abs(-7))
print("round(3.14159, 2):", round(3.14159, 2))
print("pow(2, 5):", pow(2, 5))
print("max(1, 5, 3):", max(1, 5, 3))
print("min(1, 5, 3):", min(1, 5, 3))
print("sum([1, 2, 3]):", sum([1, 2, 3]))

# math module
print("math.ceil(2.3):", math.ceil(2.3))
print("math.floor(2.7):", math.floor(2.7))
print("math.trunc(3.9):", math.trunc(3.9))
print("math.isqrt(10):", math.isqrt(10))
print("math.factorial(5):", math.factorial(5))
print("math.fmod(10, 3):", math.fmod(10, 3))
print("math.remainder(10, 3):", math.remainder(10, 3))
print("math.copysign(-2, 3):", math.copysign(-2, 3))

# Trigonometry
angle = math.pi / 4
print("math.sin(angle):", math.sin(angle))
print("math.cos(angle):", math.cos(angle))
print("math.tan(angle):", math.tan(angle))
print("math.asin(0.5):", math.asin(0.5))
print("math.acos(0.5):", math.acos(0.5))
print("math.atan(1):", math.atan(1))
print("math.atan2(1, 1):", math.atan2(1, 1))
print("math.hypot(3, 4):", math.hypot(3, 4))
print("math.degrees(math.pi):", math.degrees(math.pi))
print("math.radians(180):", math.radians(180))

# Logs & exponentials
print("math.exp(2):", math.exp(2))
print("math.expm1(1e-5):", math.expm1(1e-5))
print("math.log(100, 10):", math.log(100, 10))
print("math.log2(8):", math.log2(8))
print("math.log10(1000):", math.log10(1000))
print("math.pow(3, 3):", math.pow(3, 3))

# Special functions
print("math.gamma(5):", math.gamma(5))
print("math.lgamma(5):", math.lgamma(5))
print("math.erf(1):", math.erf(1))
print("math.erfc(1):", math.erfc(1))

# Floating point helpers
print("math.fabs(-3.5):", math.fabs(-3.5))
print("math.isclose(1.000001, 1.0, rel_tol=1e-5):", math.isclose(1.000001, 1.0, rel_tol=1e-5))
print("math.dist([0, 0], [3, 4]):", math.dist([0, 0], [3, 4]))
print("math.nextafter(1, 2):", math.nextafter(1, 2))
print("math.ulp(1.0):", math.ulp(1.0))

# Checks
print("math.isfinite(1.0):", math.isfinite(1.0))
print("math.isinf(math.inf):", math.isinf(math.inf))
print("math.isnan(math.nan):", math.isnan(math.nan))

# Constants
print("math.pi:", math.pi)
print("math.e:", math.e)
print("math.tau:", math.tau)
print("math.inf:", math.inf)
print("math.nan:", math.nan)

🧩 Tips & Notes

  • math.sqrt() returns a float, even for perfect squares.
  • math.factorial() only works with non-negative integers.
  • Trigonometric functions like math.sin() use radians, not degrees. Convert degrees using: 
math.radians(45)  # Converts 45° to radians
  • math.fabs() always returns a float, unlike abs() which preserves the original type.

🆚 math vs. numpy

Feature math numpy
Speed Fast for single values Fast for arrays
Array support ❌ No ✅ Yes
SciPy integration ❌ No ✅ Seamless
Precision Good Excellent with dtypes

Use math for simple scalar math. Switch to numpy for bulk operations or scientific computing.