Area of a Square Calculator

Q: 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

Q: 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 .

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Hanna Pamuła, PhD

Hanna PamułaPhD

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Hanna (Hania) Pamuła holds a Ph.D. in Bioacoustics / Mechanical Engineering, obtained at AGH University of Science and Technology. She has participated in research work in labs in France and the UK and presented papers at several international conferences. Hania has a penchant for photography and graphic design. When not in the office, she’s probably traveling, hiking, or out in the field, watching birds and recording their calls. See full profile

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Bogna Szyk and Adena Benn

Adena Benn

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Adena Benn is a Guyanese teacher with a degree in computer science who is always reading and learning. She loves problem-solving, everything tech, and working with teenagers. She has a passion for education and is especially interested in how children learn and the teaching methods that best suit their learning styles. She grew up on a farm in Pomeroon, Guyana, where she worked alongside her parents and siblings. As such, she is just as comfortable growing plants as teaching in the classroom. In her early life, she also gained expertise as a seamstress, which she learned from her mother. By grade 9, she had already acquired her dressmaker's certificate. Today she uses her skills to design many items for her family. In her free time, Adena loves to read, take long walks, write children’s stories and poetry, travel, or spend time with her family. See full profile

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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.

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

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:

Explanation of area of the square concept. Square units

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!

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., $11$ inches, into the side box.
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.

FAQs

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.