Lesson 9: Math Functions and Module

Built-in Math Functions

Python includes several built-in math functions that are always available without importing any modules. These are convenient for common mathematical operations:

builtin_math.py
# Absolute value (distance from zero)
print(abs(-5))      # 5
print(abs(5))       # 5
print(abs(-3.7))    # 3.7

# Rounding (to nearest integer or specified decimal places)
print(round(3.7))       # 4 (round to nearest integer)
print(round(3.4))       # 3
print(round(3.14159, 2))  # 3.14 (2 decimal places)
print(round(2.675, 2))    # 2.67 (banker's rounding)

# Min and Max (find smallest/largest value)
print(min(1, 5, 3))      # 1
print(max(1, 5, 3))      # 5
print(min([10, 5, 8, 3]))  # 3 (works with lists too)

# Power function (exponentiation)
print(pow(2, 3))        # 8 (same as 2 ** 3)
print(pow(5, 2))        # 25
print(pow(16, 0.5))    # 4.0 (square root)

# Sum function
print(sum([1, 2, 3, 4]))  # 10

The math Module

For more advanced mathematical operations, Python provides the math module. You need to import it to use its functions:

math_module.py
import math

# Mathematical constants
print(math.pi)          # 3.141592653589793 (π)
print(math.e)           # 2.718281828459045 (Euler's number)
print(math.tau)         # 6.283185... (2π)

# Square root and powers
print(math.sqrt(16))    # 4.0
print(math.sqrt(2))     # 1.4142135623730951
print(math.pow(2, 3))   # 8.0 (same as 2 ** 3)

# Rounding functions
print(math.floor(3.7))  # 3 (round down)
print(math.ceil(3.2))   # 4 (round up)
print(math.trunc(3.7))  # 3 (truncate decimal part)

# Trigonometric functions (angles in radians)
print(math.sin(math.pi/2))     # 1.0 (sin of 90 degrees)
print(math.cos(0))            # 1.0 (cos of 0 degrees)
print(math.tan(math.pi/4))     # ~1.0 (tan of 45 degrees)

# Logarithmic functions
print(math.log(100, 10))   # 2.0 (log base 10 of 100)
print(math.log(8, 2))      # 3.0 (log base 2 of 8)
print(math.log(100))       # Natural log (base e)

# Other useful functions
print(math.fabs(-5))     # 5.0 (absolute value, always float)
print(math.factorial(5))  # 120 (5! = 5*4*3*2*1)
print(math.gcd(48, 18))   # 6 (greatest common divisor)

Common Math Module Functions

Here's a comprehensive list of commonly used math functions:

math.sqrt(x) — Square root of x
math.pow(x, y) — x raised to the power of y
math.floor(x) — Largest integer ≤ x (round down)
math.ceil(x) — Smallest integer ≥ x (round up)
math.fabs(x) — Absolute value (always returns float)
math.factorial(x) — Factorial of x (x!)
math.gcd(a, b) — Greatest common divisor
math.sin(x), math.cos(x), math.tan(x) — Trigonometric functions
math.log(x, base) — Logarithm with specified base
math.pi — Mathematical constant π
math.e — Mathematical constant e

Practical Examples

Here are real-world examples of using math functions:

practical_math.py
import math

# Calculate area of a circle
radius = 5
area = math.pi * radius ** 2
print(f"Circle area: {area:.2f}")

# Calculate distance between two points
x1, y1 = 0, 0
x2, y2 = 3, 4
distance = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
print(f"Distance: {distance}")  # 5.0 (3-4-5 triangle)

# Rounding prices
price = 19.998
rounded_price = round(price, 2)
print(f"Price: ${rounded_price}")

# Finding maximum in a dataset
scores = [85, 92, 78, 96, 88]
highest = max(scores)
lowest = min(scores)
print(f"Highest: {highest}, Lowest: {lowest}")

# Converting degrees to radians for trig functions
degrees = 45
radians = math.radians(degrees)  # Convert to radians
print(f"sin({degrees}°) = {math.sin(radians):.2f}")

Built-in vs math Module

📝 When to Use What

Built-in functions (abs, round, min, max, sum): Use for basic operations that don't require importing

math module: Use for advanced mathematical operations like square roots, trigonometry, logarithms, and special constants