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

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.
Hanna Pamuła, PhD
Image of a square with side a. Area of a square
Side a
in
Area
in²
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