Python Modulo

Summary: in this tutorial, you’ll learn about the Python modulo operator (%) and how to use it effectively.

Introduction to the Python modulo operator #

Python uses the percent sign (%) as the modulo operator. The modulo operator always satisfies the following equation:

N = D * ( N // D) + (N % D)Code language: JavaScript (javascript)

In this equation:

• N is the numerator.
• D is the denominator.
• // is the floor division operator
• And % is the modulo operator

If both N and D are positive integers, the modulo operator returns the remainder of N / D. However, it is not the case for the negative numbers. Therefore, you should always stick with the above equation.

Simple Python modulo operator examples #

The following example illustrates how to use the modulo operator (%) with positive integers:

a = 16
b = 5

m = a % b
f = a // b

# show the result

print(f'{a} % {b} = {m}')  # 1
print(f'{a} // {b} = {f}')  # 3Code language: Python (python)

Output:

1
3

For positive numbers, the result is quite apparent. And you can check the equation quickly:

16 = 5 * (16 // 5) + 16 % 5
16 = 5 * 3         + 1Code language: JavaScript (javascript)

The following shows how to use the modulo operator (%) with negative integers:

a = -16
b = 5

m = a % b
f = a // b

# show the result

print(f'{a} % {b} = {m}')  # 4
print(f'{a} // {b} = {f}')  # -4Code language: Python (python)

And the equation is satisfied:

-16 = 5 * (-16 % 5) + (-16) % 5
-16 = 5 * -4        - 4

Practical Python modulo operator examples #

Let’s take some practical examples of using the modulo operator (%)

1) Using the modulo operator to check if a number is even or odd #

The following defines a function that uses the modulo operator (%) to check if a number is even:

def is_even(num):
    return num % 2 == 0
Code language: Python (python)

And the following defines a function that uses the modulo operator to check if a number is odd:

def is_odd(num):
    return num % 2 != 0
Code language: JavaScript (javascript)

2) Using the modulo operator to convert units #

The following example uses the modulo operator (%) to convert seconds to days, hours, minutes, and seconds. It can be handy if you want to develop a countdown program:

from math import floor


def get_time(total_seconds):
    return {
        'days': floor(total_seconds / 60 / 60 / 24),
        'hours': floor(total_seconds / 60 / 60) % 24,
        'minutes': floor(total_seconds / 60) % 60,
        'seconds': total_seconds % 60,
    }


print(get_time(93750))Code language: Python (python)

Output:

{'days': 1, 'hours': 2, 'minutes': 2, 'seconds': 30}Code language: JavaScript (javascript)

Summary #

• Python uses the percent sign (%) as the modulo operator.
• The modulo operator (%) always satisfies the equation N = D * ( N // D) + (N % D).