From the side
A = c²
The side multiplied by itself.
Area of a Square Calculator (Side or Diagonal)
Calculate the area of a square from the length of its side (A = s²) or its diagonal (A = d² ÷ 2). Formulas explained, finding the side from the area with a square root, tile and land examples, and results in cm², m², in² or ft².
Area
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How does this tool work?
This calculator gives the area of a square from its side or its diagonal. Use it to check an exercise, to find the surface of a paver, a tile or a square room, or to measure a square when only the diagonal can be reached, such as a screen, a tabletop or a concrete form.
A square has four equal sides and four right angles. Its area is side × side, so A = s². That is exactly where the word "squared" comes from: 5² is the area of a square with a side of 5.
With the diagonal d, the tool applies A = d² ÷ 2. This formula comes from the Pythagorean theorem: in a square, d² = s² + s² = 2s², so s² = d² ÷ 2. A square whose diagonal is 10 cm therefore has an area of 50 cm² and a side of about 7.07 cm.
The result is expressed in the square of the unit you chose. Watch the conversions: multiplying the side by 10 multiplies the area by 100. A square 1 m on a side holds 10,000 squares 1 cm on a side, hence 1 m² = 10,000 cm²; likewise 1 ft² = 144 in².
For the reverse operation, finding the side from the area, take the square root: s = √A. A square plot of 400 m² is 20 m on a side; a square hectare is 100 m on a side, and a square acre about 208.7 ft (63.6 m).
How to use this tool
Pick the measurement you know
Side if you know the length of one edge, Diagonal if you measure from one corner to the opposite corner.
Enter the value and its unit
From millimeters to kilometers, plus inches, feet and yards.
Read the area
The area appears in the matching square unit and recalculates as you type.
Formulas for the area of a square
The area can be found from the side or the diagonal, two measurements linked by √2.
From the diagonal
A = d² ÷ 2
A consequence of the Pythagorean theorem: d² = 2c².
Side from the area
c = √A
The inverse operation: the square root of the area.
Diagonal from the side
d = c × √2
The diagonal is about 1.414 times the side.
- A
- area, in square units
- c
- length of one side (also written s)
- d
- diagonal, from one corner to the opposite corner
Example: s = 12 m, A = 144 m² and d = 12√2 ≈ 16.97 m.
Use cases
Tiling and paving
Know the area of one square tile or paver to estimate how many you need per square meter or per square foot.
Rooms, plots and lots
Calculate the area of a square room or piece of land from a single measurement.
Measuring by the diagonal
Get the area of a square when only the diagonal is accessible: concrete form, tabletop, frame or panel.
Geometry exercises
Practice squares, square roots and the link between diagonal and side that comes from the Pythagorean theorem.
Examples
From the side
7 × 7 = 49 cm².
Input
s = 7 cmResult
A = 49 cm²From the diagonal
10² ÷ 2 = 100 ÷ 2 = 50 cm².
Input
d = 10 cmResult
A = 50 cm²Floor tile
You need about 2.78 tiles per square meter (1 ÷ 0.36), before adding a cutting allowance.
Input
s = 60 cmResult
A = 0.36 m²Square room
3.8² = 14.44 m² of floor to cover.
Input
s = 3.8 mResult
A = 14.44 m²Diagonal of a tabletop
1.44 ÷ 2 = 0.72 m², for a side of about 84.85 cm.
Input
d = 1.2 mResult
A = 0.72 m²Tips and best practices
- Make sure the shape really is a square: two equal sides are not enough, you also need right angles.
- To go from cm² to m², divide by 10,000.
- The diagonal of a square is always s × √2, about 1.414 times the side.
- To find the side for a target area, take the square root of the area.
- For a rhombus (equal sides but no right angles), use the diagonals formula in the geometry calculator instead.
Sources and references
- Weisstein E.W., Square (opens in a new tab), Wolfram MathWorldPage in English
- Weisstein E.W., Area (opens in a new tab), Wolfram MathWorldPage in English
- Programme de mathématiques pour le cycle 3 (opens in a new tab), Ministère de l’Éducation nationalePage in French
Frequently asked questions
What is the formula for the area of a square?
A = s × s = s², where s is the length of one side. With the diagonal d, A = d² ÷ 2.
How do you find the area of a square from its diagonal?
Square the diagonal, then divide by two. For an 8 cm diagonal: 64 ÷ 2 = 32 cm².
How do you find the side of a square from its area?
Take the square root of the area: s = √A. An area of 81 m² gives a side of 9 m; an area of 50 m² gives a side of about 7.07 m.
If I double the side, does the area double?
No, it is multiplied by four. A square 2 m on a side covers 4 m², a square 4 m on a side covers 16 m².
How many 30 cm (12 in) tiles do I need?
A 30 cm tile covers 0.09 m², so you need about 11.1 per square meter. A 12-inch tile covers exactly 1 sq ft, so 100 tiles per 100 sq ft. Round up and add 5 to 10% for cuts.
How do you find the area of a hollow square (square frame)?
Subtract the area of the inner square from that of the outer square: A = S² − s². A frame with a 50 cm outer side and a 40 cm inner side covers 2,500 − 1,600 = 900 cm². With the border width w, A = 4w × (S − w): 4 × 5 × 45 = 900 cm².
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