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Formulas for the area of a squareWhat is the area of a square?How to use the area of a square calculatorFAQsIf 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.

## Formulas for the area of a square

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

$A = a\times a = a^2$A=a×a=a2

where $a$a is a square side.

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

- $A = d^2 / 2$A=d2/2 if you know the diagonal;
- $A= P^2 / 16$A=P2/16 if the perimeter is given (you can learn how to find $P$P in every possible way with our perimeter of a square calculator);
- $A= 2 \times R^2$A=2×R2 knowing circumradius $R$R; and
- $A= 4 \times r^2$A=4×r2 in terms of the inradius $r$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}$1in. 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 $A= a^2 = 1\ \mathrm{in^2}$A=a2=1in2, 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}$4in2, and we need to use 4 times more "paint". Full chessboard area equals $64\ \mathrm{in^2}$64in2: $8\ \mathrm{in} \times 8\ \mathrm{in}$8in×8in from the formula, or it's just **64** small squares with $1\ \mathrm{in^2}$1in2 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!

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

### How do I find the area of a square given perimeter?

If you know the perimeter of a square and want to determine its area, you need to:

- Divide the perimeter by 4.
- The result is the side of the square.
- Multiply the side by itself.
- The result is the area of your square.

### How do I find the diagonal of a square given area?

To compute the length of a diagonal of a square given its area, follow these steps:

Multiply the area by

**2**.Take the square root of the result of

**step 1**.That's it! The result is the diagonal of your square. Congrats!

The formula we used here is:

**diagonal = √(2 × area)**

### What is the area of a square with diagonal 10?

The answer is **50**. This is because the formula linking the area of a square with its diagonal is:

**area = diagonal² / 2**

Hence, plugging in **diagonal = 10**, we obtain:

**area = 100 / 2 = 50**

### What is the area of a square with perimeter 52?

The answer is **169**. To arrive at this result, observe that the perimeter is equal to **52**. This means that the side of the square equals:

**side = perimeter /4 = 52 / 4 = 13**

Hence, the area is:

**area = 13² = 169**.