Area of a Square Calculator
Welcome to our Area of a Square Calculator page.
We explain how to find the area of a square and provide a quick calculator to work it out for you, step-by-step.
There is also a separate calculator which will find the length of the side of a square, if you already know the area.
Area of a Square Calculator
This calculator finds the area of a square when the side length is known.
How the Calculator Works
- Choose the length of side value: you can choose a whole number, decimal or fraction.
- You can type a fraction by typing the numerator then '/' then the denominator.
- You can type a mixed number by typing the whole-number part, then a space then the fraction part.
- Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
- Choose your units of measurement (default is none)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Area button
- You will be shown the area as a decimal (and also a fraction if you typed the length as a fraction).
Area of a Square Calculator 2
This calculator finds the side length of the square when the area is known.
How the Calculator Works
- Choose the area value: you can choose a whole number, decimal or fraction.
- Choose your units of measurement (default is none)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Side Length button
- You will be shown the side length as a decimal to the required accuracy.
Area of a Square Formula
The formula for the area of a square is: A = s2, where s is the length of one of the sides.
Area of a Square Examples
Area of a Square Example 1
Find the area of the square below.
The length of each side of the square is 13cm.
The area of a square, A = s2, where s is the length of each side.
So this means that A = 132 = 13 x 13 = 169
This means that the area of the square is 169 cm2.
Area of a Square Example 2
Find the area of the square below, giving your answer as a fraction.
The length of each side of the square is 3 ¼ inches.
The area of the square:
\[ A = (3 {1 \over 4}) ^2 = 3 {1 \over 4} \times 3 {1 \over 4} = {169 \over 16} = 10 {9 \over 16} \]
This means that the area of the square is: \[ 10 {9 \over 16} \; square \; inches \]
Area of a Square Example 3
Find the area of the square below.
The length of each side of the square is 9.3 meters.
The area of the square, A = (9.3)2 = 9.3 x 9.3 = 86.49
This means that the area of the square is 86.49 m2.
Area of a Square Example 4
Use the area of the square below to find the length of each side correct to 1 decimal place.
The area of the square is 70 cm2.
The area of a square, A = s2, where s is the length of each side.
We can rearrange this equation in terms of the side length s to give us:
\[ s = \sqrt A \]
Substituting the value of A into this equation gives us:
\[ s = \sqrt (70) = 8.3666....\]
This means that the length of each side is 8.4 cm to 1 decimal place.
Perimeter of a Square
Our Perimeter of a Square calculator will show you how to find the perimeter of squares, including ones with fractional side lengths.
There are also worked examples to help you with this skill
More Area Support and Resources
We have a range of other area worksheets and support pages for a range of different 2d shapes.
More Area & Volume Calculators
We have a range of area and volume calculators to help you find the area and volumes of a range of different 2d and 3d shapes.
Each calculator page comes with worked examples, formulas and practice worksheets.
Looking for more math calculators?
We have a wide range of free math calculators to help you.
Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.
Our calculator hub page contains links to all of our calculators!
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