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Area of a Square Calculator

Table of contents

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

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

image of area of a square with side a

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

A=a×a=a2A = a\times a = a^2

where aa is a square side.

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

  • A=d2/2A = d^2 / 2 if you know the diagonal;
  • A=P2/16A= P^2 / 16 if the perimeter is given (you can learn how to find PP in every possible way with our perimeter of a square calculator);
  • A=2×R2A= 2 \times R^2 knowing circumradius RR; and
  • A=4×r2A= 4 \times r^2 in terms of the inradius rr.

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 in1\ \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=a2=1 in2A= 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 in24\ \mathrm{in^2}, and we need to use 4 times more "paint". Full chessboard area equals 64 in264\ \mathrm{in^2}: 8 in×8 in8\ \mathrm{in} \times 8\ \mathrm{in} from the formula, or it's just 64 small squares with 1 in21\ \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., 1111 inches, into the side box.
  3. The area appears! It's 121 in2121\ \mathrm{in^2}. 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:

  1. Divide the perimeter by 4.
  2. The result is the side of the square.
  3. Multiply the side by itself.
  4. 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:

  1. Multiply the area by 2.

  2. Take the square root of the result of step 1.

  3. That's it! The result is the diagonal of your square. Congrats!

  4. 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.

Image of a square with side a. Area of a square

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