floor() and ceil() function Python

Last Updated : 16 Jan, 2026

Python’s math module provides many useful mathematical functions, including floor() and ceil(), which are commonly used for rounding numbers.

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

Note: Both functions require importing the math module: import math

Python 
import math

x = 3.7
print(math.floor(x))  
print(math.ceil(x))

Output
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 return an integer.

1. Round a List of Floats

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

Python 
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)

Output

Floor: [1, 2, 3, 4, 5]
Ceil : [2, 3, 4, 4, 6]

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.

2. Compare floor() and ceil() with Negative Numbers

Python 
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))

Output

floor(-2.3): -3
ceil(-2.3) : -2
floor(-5.9): -6
ceil(-5.9) : -5

Explanation:

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

3. Round User Input to Nearest Integer.

Python 
import math

a = 7.3
print("Rounded down using floor():", math.floor(a))
print("Rounded up using ceil():", math.ceil(a))

Output
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.

Floor and Ceil using Integer Division

Python 
x = 4.5
y = -4.5

fx = x // 1 if x >= 0 else (x // 1 if x == x // 1 else x // 1 - 1)
cx  = x // 1 if x == x // 1 else (x // 1 + 1) if x > 0 else x // 1

fy = y // 1 if y >= 0 else (y // 1 if y == y // 1 else y // 1 - 1)
cy  = y // 1 if y == y // 1 else (y // 1 + 1) if y > 0 else y // 1

print("Floor of 4.5:", fx)
print("Ceil of 4.5 :", cx)

print("Floor of -4.5:", fy)
print("Ceil of -4.5 :", cy)

Output
Floor of 4.5: 4.0
Ceil of 4.5 : 5.0
Floor of -4.5: -6.0
Ceil of -4.5 : -5.0

Explanation:

1. Floor

  • Positive: x // 1
  • Negative: subtract 1 if x is not already integer (x // 1 - 1)

2. Ceil

  • Positive: x // 1 + 1 if not integer
  • Negative: just x // 1
Comment

Explore