This article will explain (*in the simplest terms possible*) what **modulus** and **modulo** mean and how they are calculated in the PHP programming language.

## Modulus and Modulo are NOT the Same Things!

There’s a bit of confusion about this, and it seems that in some places, the terms are used interchangeably – 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**.

### Calculating the Modulus in PHP

The abs() function in PHP calculate the absolute value of a number. Here it is in use:

abs(3);

Simply pass a number 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.**

## 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 PHP

In PHP, it 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 have any long-term side effects on your health, but it’ll make searching for solutions online *really* frustrating.