This tutorial will explain (hopefully in the simplest terms possible) what modulus and modulo mean and how they can be calculated in the Python programming language.
Modulus and Modulo are Different Things!
There’s a bit of confusion about this, and it seems that in some places, the terms modulus and modulo are used in place of each other – this is wrong (and confused me too – hence this article)!
What is Modulus?
In mathematics, the modulus is the absolute value of a number. It’s the non-negative value of a number – or its distance from 0 (zero).
So, the modulus of 3 is 3, and the modulus of -3 is also 3. So, it’s essentially just the number without a negative sign.
Calculating the Modulus in Python
Simply pass any number (float or integer) to the abs() function, and the absolute value (modulus) of the number will be returned.
What Is It Used For?
The modulus of a number is frequently used in physics calculations – particularly when calculating momentum and collisions. The sign (positive or negative) of a number representing movement may indicate its direction, while the modulus represents the speed of movement.
If you’re coding video games, you’ll certainly put it to good use – most games use a basic physics engine to calculate movement and send projectiles flying across the screen.
What is Modulo?
In programming, the modulo is an arithmetic operator – it calculates the remainder left when one number is divided by another.
What is a Remainder?
The remainder is a mathematical term – it’s the amount left-over when one number has been divided by another if the first number cannot be divided by the second exactly.
So, 6 ÷ 3 has a remainder of 0, as 6 can be cleanly divided by 3 with nothing left over.
However, 7 ÷ 3 has a remainder of 1, 7 cannot be divided into 3 equal values, the nearest number less than 7 which can be cleanly divided by 3 is 6 – leaving 1 remainder.
Calculating the Modulo in Python
In the Python programming language, the modulo is represented by the % (percent) symbol.
Here it is in action:
remainder = 7 % 3; # 7 can be divided by 3 twice, leaving a remainder of 1
Above, the variable remainder will be given a value of 1 – the remainder when 7 has been divided by 3.
Don’t Mix Them Up!
Mixing the terms modulus and modulo up probably won’t do you any harm, but it’ll make searching for solutions online really frustrating.