math

Updated March 13, 2026· Modules

mathstdlibnumericaltrigonometry

The math module is part of Python’s standard library. It provides functions for common mathematical operations including rounding, trigonometric calculations, logarithms, and constants like pi and e.

Syntax

import math

Key Functions

Numerical Operations

Function	Signature	Description
`ceil()`	`ceil(x)`	Returns the smallest integer greater than or equal to x
`floor()`	`floor(x)`	Returns the largest integer less than or equal to x
`sqrt()`	`sqrt(x)`	Returns the square root of x
`pow()`	`pow(x, y)`	Returns x raised to the power of y
`factorial()`	`factorial(n)`	Returns n! (n factorial)
`gcd()`	`gcd(a, b)`	Returns the greatest common divisor of a and b
`fabs()`	`fabs(x)`	Returns the absolute value of x as a float

Trigonometric Functions

Function	Signature	Description
`sin()`	`sin(x)`	Returns the sine of x (x in radians)
`cos()`	`cos(x)`	Returns the cosine of x (x in radians)
`tan()`	`tan(x)`	Returns the tangent of x (x in radians)
`degrees()`	`degrees(x)`	Converts radians to degrees
`radians()`	`radians(x)`	Converts degrees to radians

Logarithmic and Exponential

Function	Signature	Description
`log()`	`log(x[, base])`	Returns the natural logarithm of x, or to the given base
`log10()`	`log10(x)`	Returns the base-10 logarithm of x
`log2()`	`log2(x)`	Returns the base-2 logarithm of x
`exp()`	`exp(x)`	Returns e raised to the power of x

Constants

Constant	Value	Description
`pi`	3.14159…	The mathematical constant π
`e`	2.71828…	The mathematical constant e
`tau`	6.28318…	The mathematical constant τ (2π)
`inf`	∞	Positive infinity
`nan`	NaN	Not a Number

Examples

Basic numerical operations

import math

# Rounding
print(math.ceil(4.2))   # 5
print(math.floor(4.8))  # 4
print(math.trunc(4.8))  # 4

# Square root and power
print(math.sqrt(16))     # 4.0
print(math.pow(2, 3))   # 8.0
print(math.pow(27, 1/3))  # 3.0 (cube root)

# Factorial and gcd
print(math.factorial(5))  # 120
print(math.gcd(48, 18))  # 6

Trigonometry

import math

# Sine, cosine, tangent (input in radians)
print(math.sin(math.pi / 2))  # 1.0
print(math.cos(math.pi))      # -1.0
print(math.tan(math.pi / 4)) # 1.0

# Convert between degrees and radians
print(math.degrees(math.pi))    # 180.0
print(math.radians(90))         # π/2 ≈ 1.5708

Logarithms

import math

# Natural logarithm
print(math.log(math.e))    # 1.0
print(math.log(1))        # 0.0

# Base-10 logarithm
print(math.log10(100))    # 2.0
print(math.log10(1000))   # 3.0

# Base-2 logarithm
print(math.log2(8))       # 3.0
print(math.log2(1024))    # 10.0

Using constants

import math

# Calculate area of a circle
radius = 5
area = math.pi * radius ** 2
print(area)  # 78.5398...

# Calculate circumference
circumference = 2 * math.pi * radius
print(circumference)  # 31.4159...

Common Patterns

Checking if a number is finite or infinite

import math

print(math.isfinite(10))     # True
print(math.isinf(math.inf))  # True
print(math.isnan(math.nan))  # True

Summing with precision

import math

values = [0.1] * 10
total = sum(values)  # May not be exactly 1.0
print(total)  # 0.9999999999999999

# Use math.fsum for floating-point precision
print(math.fsum(values))  # 1.0

Finding the hypotenuse

import math

# Pythagorean theorem: c = sqrt(a² + b²)
a, b = 3, 4
c = math.hypot(a, b)
print(c)  # 5.0