How to Round Down in Python

Master math.floor() and downward rounding techniques

Understanding Round Down Operations

Rounding down means always moving toward the smaller value (toward negative infinity). In Python, the primary method for rounding down is math.floor(), but there are several techniques depending on your specific needs.

This guide covers all methods for rounding down in Python, including math.floor(), int() for positive numbers, custom functions for decimal places, and important differences with negative numbers.

1. math.floor() - The Primary Method

Syntax

math.floor(x)

The math.floor() function returns the largest integer less than or equal to x. It always rounds DOWN toward negative infinity.

Basic Examples:

import math

# Positive numbers - round down to lower integer
print(math.floor(3.9))         # Output: 3
print(math.floor(3.1))         # Output: 3
print(math.floor(3.0))         # Output: 3 (already integer)
print(math.floor(7.999))       # Output: 7

# Negative numbers - toward negative infinity
print(math.floor(-3.1))        # Output: -4 (down means more negative)
print(math.floor(-3.9))        # Output: -4
print(math.floor(-2.01))       # Output: -3

# Edge cases
print(math.floor(0))           # Output: 0
print(math.floor(0.1))         # Output: 0
print(math.floor(-0.1))        # Output: -1

Important: Negative Number Behavior

math.floor() always rounds toward negative infinity. For negative numbers, this means rounding to a MORE NEGATIVE value (which is mathematically "down"):

# -3.1 is between -4 and -3
# Floor goes to -4 (toward -∞)
print(math.floor(-3.1))   # -4

# -3.9 is between -4 and -3
# Floor goes to -4 (toward -∞)
print(math.floor(-3.9))   # -4

Step-by-Step Tutorial:

Step 1: Import the math module

import math

Step 2: Call floor() with your number

result = math.floor(5.7)

Step 3: Use the result

print(result) # 5

2. int() - For Positive Numbers Only

Syntax

int(x)

The built-in int() function truncates toward zero. For positive numbers, this is the same as rounding down. For negative numbers, it's different!

Examples:

# Positive numbers - int() rounds down (same as floor)
print(int(3.9))            # Output: 3
print(int(3.1))            # Output: 3
print(int(7.999))          # Output: 7

# Negative numbers - int() rounds UP toward zero (different!)
print(int(-3.9))           # Output: -3 (not -4!)
print(int(-3.1))           # Output: -3 (not -4!)

# Compare to floor()
print(math.floor(-3.9))    # Output: -4
print(int(-3.9))           # Output: -3

Warning: Don't Use int() for Negative Numbers

If you need true "round down" behavior for all numbers (including negatives), always use math.floor(). The int() function truncates toward zero, which rounds UP for negative numbers.

# WRONG for rounding down negative numbers
int(-3.7)          # -3 (rounds UP toward zero)

# CORRECT for rounding down all numbers
math.floor(-3.7)   # -4 (rounds DOWN toward -∞)

Comparison: math.floor() vs int() vs math.trunc()

Understanding the differences between these three functions is crucial for correct rounding behavior:

Function	3.7	-3.7	Direction	Use Case
math.floor()	3	-4	Toward -∞	True round down
int()	3	-3	Toward 0	Positive numbers only
math.trunc()	3	-3	Toward 0	Remove decimal part

import math

number = 3.7
print(f"math.floor({number}) = {math.floor(number)}")   # 3
print(f"int({number}) = {int(number)}")                 # 3
print(f"math.trunc({number}) = {math.trunc(number)}")   # 3

number = -3.7
print(f"math.floor({number}) = {math.floor(number)}")   # -4 ← Only this rounds DOWN
print(f"int({number}) = {int(number)}")                 # -3
print(f"math.trunc({number}) = {math.trunc(number)}")   # -3

Round Down to Decimal Places

math.floor() only rounds to integers. To round down to a specific number of decimal places, you need a custom function:

import math

def floor_to_decimals(number, decimals=0):
    """
    Round DOWN to specified decimal places.

    Args:
        number: The number to round
        decimals: Number of decimal places (default: 0)

    Returns:
        Number rounded down to specified decimal places
    """
    multiplier = 10 ** decimals
    return math.floor(number * multiplier) / multiplier

# Examples
print(floor_to_decimals(3.999, 2))      # Output: 3.99
print(floor_to_decimals(3.999, 1))      # Output: 3.9
print(floor_to_decimals(3.999, 0))      # Output: 3.0

print(floor_to_decimals(12.9876, 2))    # Output: 12.98
print(floor_to_decimals(12.9876, 3))    # Output: 12.987

# Negative numbers
print(floor_to_decimals(-3.999, 2))     # Output: -4.00
print(floor_to_decimals(-12.9876, 2))   # Output: -12.99

How It Works:

Step 1: Multiply by 10^decimals

Move the decimal point right

3.999 × 100 = 399.9

Step 2: Apply floor()

Round down to integer

floor(399.9) = 399

Step 3: Divide by 10^decimals

Move the decimal point back

399 / 100 = 3.99

Real-World Use Cases

1. Floor Division - Complete Groups

import math

# Calculate complete groups
total_items = 47
items_per_box = 10

complete_boxes = math.floor(total_items / items_per_box)
print(f"Complete boxes: {complete_boxes}")  # Output: 4

remaining = total_items % items_per_box
print(f"Items remaining: {remaining}")      # Output: 7

2. Array Indexing - Valid Indices

import math

# Calculate array index from floating point position
position = 7.8
index = math.floor(position)

arr = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i']
print(f"Element at position {position}: {arr[index]}")
# Output: Element at position 7.8: h

# Another example: pixel coordinates
pixel_x = 123.7
pixel_y = 456.2
x_index = math.floor(pixel_x)
y_index = math.floor(pixel_y)
print(f"Pixel at ({x_index}, {y_index})")  # (123, 456)

3. Pagination - Page Numbers

import math

def get_page_number(item_index, items_per_page):
    """Calculate which page an item is on (0-indexed)"""
    return math.floor(item_index / items_per_page)

# Examples
print(f"Item 0 is on page: {get_page_number(0, 10)}")    # 0
print(f"Item 9 is on page: {get_page_number(9, 10)}")    # 0
print(f"Item 10 is on page: {get_page_number(10, 10)}")  # 1
print(f"Item 25 is on page: {get_page_number(25, 10)}")  # 2

4. Conservative Price Estimates

import math

def floor_to_decimals(number, decimals):
    multiplier = 10 ** decimals
    return math.floor(number * multiplier) / multiplier

# Round down profit estimates (conservative)
projected_profit = 1234.89
conservative_estimate = floor_to_decimals(projected_profit, 0)
print(f"Conservative estimate: {conservative_estimate}")
# Output: 1234.0

# Round down discounts (customer-friendly)
original_price = 99.99
discount_rate = 0.15
max_discount = floor_to_decimals(original_price * discount_rate, 2)
print(f"Maximum discount: {max_discount}")
# Output: 14.99

5. Time/Duration Calculations

import math

# Calculate complete hours worked
minutes_worked = 475
complete_hours = math.floor(minutes_worked / 60)
remaining_minutes = minutes_worked % 60

print(f"Worked: {complete_hours}h {remaining_minutes}m")
# Output: Worked: 7h 55m

# Calculate number of complete days
hours = 73.5
complete_days = math.floor(hours / 24)
print(f"Complete days: {complete_days}")
# Output: Complete days: 3

Common Mistakes to Avoid

❌ Mistake 1: Using int() for Negative Numbers

# WRONG - int() rounds toward zero, not down
def round_down(x):
    return int(x)  # Fails for negative numbers!

print(round_down(-3.7))  # -3 (should be -4)

✓ Correct:

import math

def round_down(x):
    return math.floor(x)  # Works for all numbers

print(round_down(-3.7))  # -4 (correct!)

❌ Mistake 2: Forgetting to Import math

# WRONG - NameError
result = floor(3.7)  # NameError: name 'floor' is not defined

✓ Correct:

import math

result = math.floor(3.7)  # Works!

❌ Mistake 3: Using // Instead of floor()

# Similar but not identical for negative numbers with decimals
print(3.7 // 1)    # 3.0 (works)
print(-3.7 // 1)   # -4.0 (works)

# But // returns float if either operand is float
print(type(3.7 // 1))  # <class 'float'>
print(type(math.floor(3.7)))  # <class 'int'>

Best Practices

✓

Always Use math.floor() for True Round Down

math.floor() works correctly for both positive and negative numbers. Avoid int() unless you're certain you only have positive numbers.

✓

Create Helper Functions for Decimal Places

Wrap the multiply-floor-divide pattern in a reusable function for cleaner code.

✓

Test with Negative Numbers

Always test your rounding logic with negative numbers to ensure it behaves as expected.

✓

Document Your Rounding Behavior

Make it clear in comments and documentation how your code handles rounding, especially edge cases.

Understanding Round Down Operations

1. math.floor() - The Primary Method

Syntax

Basic Examples:

Important: Negative Number Behavior

Step-by-Step Tutorial:

Step 1: Import the math module

Step 2: Call floor() with your number

Step 3: Use the result

2. int() - For Positive Numbers Only

Syntax

Examples:

Warning: Don't Use int() for Negative Numbers

Comparison: math.floor() vs int() vs math.trunc()

Round Down to Decimal Places

How It Works:

Step 1: Multiply by 10^decimals

Step 2: Apply floor()

Step 3: Divide by 10^decimals

Real-World Use Cases

1. Floor Division - Complete Groups

2. Array Indexing - Valid Indices

3. Pagination - Page Numbers

4. Conservative Price Estimates

5. Time/Duration Calculations

Common Mistakes to Avoid

❌ Mistake 1: Using int() for Negative Numbers

❌ Mistake 2: Forgetting to Import math

❌ Mistake 3: Using // Instead of floor()

Best Practices

Always Use math.floor() for True Round Down

Create Helper Functions for Decimal Places

Test with Negative Numbers

Document Your Rounding Behavior

Related Python Guides

How to Round Numbers in Python

Python Rounding Overview

How to Round Up in Python

Python Round to 2 Decimals

JS Round to 2 Decimals

How to Round in Java