{"id":909,"date":"2020-11-01T08:47:41","date_gmt":"2020-11-01T08:47:41","guid":{"rendered":"https:\/\/www.pythontutorial.net\/?page_id=909"},"modified":"2025-03-27T15:10:19","modified_gmt":"2025-03-27T15:10:19","slug":"python-floor-division","status":"publish","type":"page","link":"https:\/\/www.pythontutorial.net\/advanced-python\/python-floor-division\/","title":{"rendered":"Python Floor Division"},"content":{"rendered":"\n

Summary<\/strong>: in this tutorial, you’ll learn about Python floor division operator (\/\/) or mod.<\/p>\n\n\n\n

Introduction to Python floor division #<\/a><\/h2>\n\n\n\n

Suppose you have a division of two integers:<\/p>\n\n\n

101 \/ 4<\/code><\/span><\/pre>\n\n\n
In this division, 101 is called a numerator (N<\/code>) and 4 is called a denominator (D<\/code>).<\/p>\n\n\n\n
The integer division 101 \/ 4 returns 25 with the remainder 1. In other words:<\/p>\n\n\n
101 \/ 4 = 25 with remainder 1<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
Or put it in another way:<\/p>\n\n\n
101 = 4 * 25 + 1<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
Python uses two operators \/\/<\/code> and % <\/code>that returns the result of the division:<\/p>\n\n\n
101 \/\/ 4 = 25\n101 % 4 = 1<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
The \/\/<\/code> is called the floor division<\/strong> operator or div. And the %<\/code> is called the modulo<\/strong> operator or mod.<\/p>\n\n\n\n
Both floor division and modulo operators satisfy the following equation:<\/p>\n\n\n
101 = 4 * (101 \/\/ 4) + (101 % 4)\n101 = 4 * 25         + 1<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
Generally, if N<\/code> is the numerator and D<\/code> is the denominator, then the floor division and modulo operators always satisfy the following equation:<\/p>\n\n\n
N = D * ( N \/\/ D) + (N % D)<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
The floor division in Python #<\/a><\/h2>\n\n\n\n
To understand the floor division, you first need to understand the floor of a real number.<\/p>\n\n\n\n
The floor of a real number is the largest integer less than or equal to the number. In other words:<\/p>\n\n\n
floor(r) = n, n is an integer and n <= r <\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
For example, the floor of 3.4 is 3 because 3 is the largest integer less than or equal to 3.4. The floor of 3.9 is also 3.  And the floor of 3 is 3 obviously:<\/p>\n\n\n
floor(3.4) = 4\nfloor(3.9) = 3\nfloor(3) = 3<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
For the positive numbers, it would be easy to understand the definition. However, you should pay attention when it comes to negative numbers.<\/p>\n\n\n\n
For example, the floor of -3.4<\/code> returns -4<\/code>, not -3<\/code> based on the floor definition. Similarly, the floor of -3.9<\/code> also returns -4<\/code> .<\/p>\n\n\n
floor(-3.4) = -4\nfloor(-3.9) = -4\nfloor(-3) = -3<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
The floor division can be defined as:<\/p>\n\n\n
n \/\/ d = floor(n\/d)<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
Notice that the floor division of a number is not always the same as truncation. The floor division is the same as truncation only when the numbers are positive.<\/p>\n\n\n\n
Python floor division operator examples #<\/a><\/h2>\n\n\n\n
The following example uses the floor division operators with positive and negative integers:<\/p>\n\n\n
a = 10\nb = 3\n\nprint(a\/\/b)  # 3\n\na = -10\nb = -3\n\nprint(a\/\/b)  # 3\n\na = 10\nb = -3\nprint(a\/\/b)  # -4\n\na = -10\nb = 3\nprint(a\/\/b)  # -4\n<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
Output:<\/p>\n\n\n
3\n3\n-4\n-4<\/code><\/span>Code language:<\/span> plaintext<\/span> (<\/span>plaintext<\/span>)<\/span><\/small><\/pre>\n\n\n
The following table illustrates the floor division of two integers a<\/code> and b<\/code>:<\/p>\n\n\n\n
a<\/th>b<\/th>a \/\/ b<\/th><\/tr><\/thead>
10<\/td>3<\/td>3<\/td><\/tr>
-10<\/td>-3<\/td>3<\/td><\/tr>
10<\/td>-3<\/td>-4<\/td><\/tr>
-10<\/td>3<\/td>-4<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Python math.floor() function #<\/a><\/h2>\n\n\n\n
The floor()<\/code> function of the math<\/code> module returns the floor division of two integers. For example:<\/p>\n\n\n
from<\/span> math import<\/span> floor\n\na = 10<\/span>\nb = 3<\/span>\n\nprint(a\/\/b)  # 3<\/span>\nprint(floor(a\/b))  # 3<\/span>\n<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
Output:<\/p>\n\n\n
3\n3<\/code><\/span><\/pre>\n\n\n
The floor()<\/code> function returns the same result as the floor division operator (\/\/<\/code>). It’s also true for the negative numbers:<\/p>\n\n\n
from<\/span> math import<\/span> floor\n\na = 10<\/span>\nb = -3<\/span>\n\nprint(a\/\/b)  # -4<\/span>\nprint(floor(a\/b))  # -4<\/span>\n<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
Output:<\/p>\n\n\n
-4\n-4<\/code><\/span><\/pre>\n\n\n
Summary #<\/a><\/h2>\n\n\n\n
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  • Python uses \/\/ as the floor division operator and %<\/code> as the modulo operator.<\/li>\n\n\n\n
  • If the numerator is N and the denominator D, then this equation N = D * ( N \/\/ D) + (N % D)<\/code> is always satisfied.<\/li>\n\n\n\n
  • Use floor division operator \/\/<\/code> or the floor()<\/code> function of the math<\/code> module to get the floor division of two integers.<\/li>\n<\/ul>\n
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Try it<\/a><\/p>\n\n\n\n
Try it<\/a><\/p>\n\n\n\n
Try it<\/a><\/p>\n\n\n\n
This tutorial focuses on the floor division operator. You’ll learn about the modulo operator in the following tutorial<\/a>.<\/p>\n\n\n\n