Floor Division Calculator

Welcome to the floor division calculator, which will help you with this very practical math operation. Here, you will understand:

• How to do floor division;
• What the difference between division and floor division is;
• How it shows up in real-life situations; and
• Why is it called this way?

If you are keen to learn floor division, you are in the right place!

Floor division, a.k.a. division with remainder, is an operation in which you round down the result of normal division to the nearest integer (a.k.a. whole number). So, the meaning of floor division is a type of division in which you always get an integer answer.

Is the above process familiar to you? Yes, you guessed right — we can speak of the floor and ceiling functions. To learn more about them, check out our floor function calculator and ceiling function calculator.

Carrying out floor division is really easy! Let's see how to do floor division in an example. To show that the floor division of 13 by 4 is 3, you have to perform these simple steps:

1. Divide 13 by 4 as usual, either by hand or using long division. You will get 3.25. If you forgot how to do long division, it is never too late to try out our long division calculator.

2. If you already have an integer in Step 1, there is nothing more to do. However, this is not the case in this floor division example.

3. Take the largest integer less than or equal to 3.25. You will be left with 3, a whole number, and this is what you are looking for!

Whether you know it or not, you carry out floor division all the time. Imagine you want to bring all your friends safely home from a party. The floor division is all you need to book the right number of cabs!

Each cab can take 4 people, the driver taking the fifth seat. So if you need to transport 13 friends, they will fill up 3 cabs. The remaining person will need to take the fourth cab, so 4 is the number of taxis to call. In this example, the number 3 of full cabs results from floor division (called quotient). The solo person to sit in the fourth cab is the remainder.

Or suppose you want to share some candies equally between your 4 siblings. If you have 13 chocolate bars to divide out, you should give 3 candies to each sibling. This is exactly what you get from the floor division! Of course, you keep the single remaining chocolate bar to yourself 😎

Useful, isn't it? Our floor division calculator can help you with all of that!

Here is a neat formula for floor division that underlies our floor division calculator:

where:

• Dividend — Number that we divide;
• Divisor — Number that we divide by; and
• $\lfloor x \rfloor$ — Integer part or floor of a number $x$. As the name suggests, $\lfloor x \rfloor$ is the largest integer smaller than or equal to $x$. On the other hand, ceiling of $x$ is denoted by $\lceil x \rceil$ and is the smallest integer greater than or equal to $x$.

The full relationship between the dividend, divisor, quotient, and remainder can be recast as follows:

Floor division can be performed in various programming languages. The table below shows some of the more popular ones, assuming dividend x and divisor y are positive integers.

You can notice that the integer division automatically floors for C, C++, and Java. If you're dealing with decimals (float or double) or negative numbers, you must use the floor functions from respective libraries.

Also, the floor division operator in Python, //, is convenient for writing quick and clear code.