# Modulus (Mod), Modulo and PHP – Explanation and Code Examples

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 17 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.

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