Area of a Square Calculator

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Nov 26, 2022

If you forgot how to find the area of a square, you're in the right place - this simple area of a square calculator is the answer to your problems. Whether you want to find the area knowing the square side or you need to calculate the side from a given area, this tool lends a helping hand. Read on and refresh your memory to find out what is the area of a square and to learn the formula behind the calculator. If you also need to calculate the diagonal of a square, check out this square calculator.

How to find the area of a square - formulas

The area of a square is the product of the length of its sides:

$A = a\times a = a^2$

where $a$ is a square side.

Other formulas also exist. Depending on which parameter is given, you can use the following equations:

• $A = d^2 / 2$ if you know the diagonal;
• $A= P^2 / 16$ if the perimeter is given (you can learn how to find $P$ in every possible way with our perimeter of a square calculator);
• $A= 2 \times R^2$ knowing circumradius $R$; and
• $A= 4 \times r^2$ in terms of the inradius $r$.

What is the area of a square?

The area of a square is the number of square units needed to completely fill a square. To understand that definition, let's have a look at this picture of a chessboard:

The board has a squared shape, with its side divided into eight parts, in total, it consists of 64 small squares. Assume that one small square has a side length equal to $1\ \mathrm{in}$. The area of the square may be understood as the amount of paint necessary to cover the surface. So, from the formula for the area of a square, we know that $A= a^2 = 1\ \mathrm{in^2}$, and it's our unit of area in the chessboard case (amount of paint). The area of a 2 x 2 piece of the chessboard is then equal to 4 squares - so it's $4\ \mathrm{in^2}$, and we need to use 4 times more "paint". Full chessboard area equals $64\ \mathrm{in^2}$: $8\ \mathrm{in} \times 8\ \mathrm{in}$ from the formula, or it's just 64 small squares with $1\ \mathrm{in^2}$ area - so we need 64 times more "paint" than for one single square.

You may also be interested in checking out the area of the largest square inscribed in a circumference with our square in a circle calculator!

How to use the area of a square calculator

Let's give the area of a square calculator a try!

1. Find out the given value. In our example, assume we know the side and want to calculate the area.
2. Type it into the proper box. Enter the value, e.g., $11$ inches, into the side box.
3. The area appears! It's $121\ \mathrm{in^2}$. If you are interested in how many square feet it is, change the unit by clicking on the unit name.
Hanna Pamuła, PhD
Side a
in
Area
in²
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