Created by Hanna Pamuła, PhD candidate
Reviewed by Bogna Szyk
Last updated: Aug 29, 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 area and 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:
- area = a * a = a², where a is a square side
Other formulas also exist. Depending on which parameter is given, you can use the following equations:
- area = d² / 2 if you know the diagonal
- area = perimeter² / 16 if the perimeter is given
- area = 2 * R² knowing circumradius R
- area = 4 * r² 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 in. The area of such 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 area = a² = 1 in², and it's our unit of area in chessboard case (amount of paint). The area of 2x2 piece of the chessboard is then equal to 4 squares - so it's 4 in² and we need to use 4 times more "paint". Full chessboard area equals 84 in²: 8 in * 8 in from the formula or it's just 64 small squares with 1 in² area - so we need 64 times more "paint" than for one single square.
You may also be interested to check out the area of the largest square in a circle!
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 we want to calculate the area.
- Type it into proper box. Enter the value, e.g. 11 inches, into side box.
- The area appears! It's 121 in². If you are interested how many square feet it is, change the unit by clicking on the unit name.
Hanna Pamuła, PhD candidate
AreaArea of a rectangleArea of crescent… 18 more
What is the area of a square that is 16 inches on a side? How big is a 16 inch square?
Units
Area of a 16″ by 16″ square
256 | square inches |
1.7778 | square feet |
0.19753 | square yards |
1,651.6 | square centimeters |
0.16516 | square meters |
(results may be rounded)
Area of a Square Formula
The area of a square is the length of one side squared.
Area = Side2
Side
Area by Length of Sides
(results are rounded)
16.0 in | 256.0 | 1.778 | 1,652 |
16.1 in | 259.2 | 1.800 | 1,672 |
16.2 in | 262.4 | 1.823 | 1,693 |
16.3 in | 265.7 | 1.845 | 1,714 |
16.4 in | 269.0 | 1.868 | 1,735 |
16.5 in | 272.3 | 1.891 | 1,756 |
16.6 in | 275.6 | 1.914 | 1,778 |
16.7 in | 278.9 | 1.937 | 1,799 |
16.8 in | 282.2 | 1.960 | 1,821 |
16.9 in | 285.6 | 1.983 | 1,843 |