floor() and ceil() function Python

Python provides a built-in math module that includes many useful mathematical functions and constants. It is commonly used for operations such as rounding numbers, working with trigonometric functions, performing logarithmic calculations, and more."

Among these are two commonly used functions:

• floor(): Rounds a number down to the nearest integer, for example, floor() of 3.3 will be 3.
• ceil(): Rounds a number up to the nearest integer, for example, ceil() of 3.3 will be 4.

These functions are part of the math module, so you need to import it before using them. Let's look at an example:

import math

x = 3.7

print(math.floor(x))  
print(math.ceil(x))   

3
4

Explanation:

• floor(3.7) returns 3 because 3 is the greatest integer less than or equal to 3.7.
• ceil(3.7) returns 4 because 4 is the smallest integer greater than or equal to 3.7.

Syntax

math.floor(number)
math.ceil(number)

Parameters:

• number: A float or integer value.

Return Type: Both functions return an integer value.

Examples of floor() and ceil()

Example 1: Round a List of Floats Down and Up

Let’s take a list of floating-point numbers and apply both floor() and ceil() to each value.

import math

a = [1.1, 2.5, 3.9, 4.0, 5.8]

fl = list(map(math.floor, a))
cl = list(map(math.ceil, a))

print("Floor:", fl)
print("Ceil :", cl)

('Floor:', [1.0, 2.0, 3.0, 4.0, 5.0])
('Ceil :', [2.0, 3.0, 4.0, 4.0, 6.0])

Explanation:

• math.floor(1.1) returns 1, and math.ceil(1.1) returns 2, and so on.
• map() function applies floor and ceil to each element of the list.

Example 2: Compare floor() and ceil() with Negative Numbers

import math

a = -2.3
b = -5.9

print("floor(-2.3):", math.floor(a))
print("ceil(-2.3) :", math.ceil(a))

print("floor(-5.9):", math.floor(b))
print("ceil(-5.9) :", math.ceil(b))

('floor(-2.3):', -3.0)
('ceil(-2.3) :', -2.0)
('floor(-5.9):', -6.0)
('ceil(-5.9) :', -5.0)

Explanation:

• floor() always rounds towards negative infinity.
• ceil() always rounds towards positive infinity.

Example 3: Round User Input to Nearest Integer.

import math

a = float(input("Enter a number: "))

print("Rounded down using floor():", math.floor(a))
print("Rounded up using ceil():", math.ceil(a))

Suppose the user inputs 7.3, then the output will be:

Rounded down using floor(): 7
Rounded up using ceil(): 8

Computing Floor and Ceil Without Importing math

Apart from using the math module, we can also compute the floor and ceil of a float using basic arithmetic operations like floor division (//) and addition.

Concept:

• x // 1 returns the largest integer less than or equal to x - similar to math.floor(x).
• To get the ceiling, just add 1 to the floor value (i.e., x // 1 + 1).

Note: This method works well for positive numbers. For negative numbers, it may not give accurate ceiling values.

Example: Floor and Ceil using Integer Division

x = 4.5

f = x // 1
print(f)

c = x // 1 + 1
print(c)  

4.0
5.0

Explanation:

• 4.5 // 1 gives 4.0, which is the floor value.
• 4.5 // 1 + 1 gives 5.0, which is the ceil value.