Area of a square
A = s² = s × sMultiply the side length by itself. If the side is 4 meters, the area is 16 square meters.
Square Area Calculator
Calculate the area, perimeter, and diagonal of a square in seconds. Enter the side length, choose your measurement units, and get instant results with formulas, worked examples, and area conversions. You can also calculate the side length when you know the area.
Area = Side²
Perimeter = 4 × Side
Diagonal calculator
Unit conversion
Free and instant
Calculate square measurements
Enter the side length or choose to calculate it from a known area.
A = s²
Multiply the side length by itself to calculate the square's area.
Your square results
All results update when you calculate or change an input.
Square area
25.00
m²
Based on a side length of 5 m.
Side length
5.00 m
Perimeter
20.00 m
Diagonal
7.07 m
Area in square meters
25.00 m²
Area in square feet
269.10 ft²
Diagonal ÷ side
√2 ≈ 1.4142
A = 5 × 5 = 25 m²
Square the side length to calculate the area.
Calculation steps
- Side length = 5 m.
- Area = 5 × 5 = 25 m².
- Perimeter = 4 × 5 = 20 m.
- Diagonal = 5 × √2 ≈ 7.07 m.
Square area formulas
A square is a quadrilateral with four equal sides and four right angles. Because all its sides are equal, you only need one measurement to calculate its area, perimeter, and diagonal.
Perimeter of a square
P = 4sMultiply the side length by four to find the total distance around the square.
Diagonal of a square
d = s√2Multiply the side length by the square root of two to find the diagonal between opposite corners.
Side from area
s = √ATake the positive square root of the area to find the side length of a square.
Area from perimeter
A = (P ÷ 4)²Divide the perimeter by four to find the side length, then square that value.
Area from diagonal
A = d² ÷ 2Square the diagonal and divide by two to calculate the area of a square.
Square area examples
Use these examples to understand how side length determines the area, perimeter, and diagonal of a square.
| Side length | Area calculation | Area | Perimeter | Diagonal (approx.) |
|---|---|---|---|---|
| 2 m | 2 × 2 | 4 m² | 8 m | 2.83 m |
| 3 cm | 3 × 3 | 9 cm² | 12 cm | 4.24 cm |
| 5 m | 5 × 5 | 25 m² | 20 m | 7.07 m |
| 10 ft | 10 × 10 | 100 ft² | 40 ft | 14.14 ft |
| 12 cm | 12 × 12 | 144 cm² | 48 cm | 16.97 cm |
Square area unit conversions
Area units are squared length units. When converting square measurements, square the linear conversion factor. For example, 1 meter equals 100 centimeters, so 1 m² equals 10,000 cm².
| Area unit | Equivalent in square meters | Common use |
|---|---|---|
| 1 mm² | 0.000001 m² | Small parts and precision measurements |
| 1 cm² | 0.0001 m² | Small surfaces and craft projects |
| 1 m² | 1 m² | Rooms, floors, and furniture |
| 1 km² | 1,000,000 m² | Large plots and geographic areas |
| 1 in² | 0.00064516 m² | Small objects and manufactured parts |
| 1 ft² | 0.09290304 m² | Flooring and property measurements |
| 1 yd² | 0.83612736 m² | Carpets and fabric |
| 1 acre | 4,046.8564224 m² | Land and property |
| 1 hectare | 10,000 m² | Agriculture and larger land areas |
How to calculate the area of a square
Calculating square area is straightforward because all four sides have the same length.
1. Measure one side
Measure one side of the square and record the value and unit. Since all sides are equal, no second measurement is necessary.
2. Multiply the side by itself
Use the formula A = s × s. For a side length of 6 meters, calculate 6 × 6.
3. Write the answer in square units
The area of a square with a 6-meter side is 36 m². Use the squared version of your length unit.
Example: A = 6² = 6 × 6 = 36 m²
A square measuring 6 meters on each side has an area of 36 square meters and a perimeter of 24 meters.
Where square area calculations are useful
Flooring and renovation
Estimate the area of square rooms, tiles, patios, and other square surfaces before buying materials.
Gardening
Calculate the surface area of square garden beds, planting plots, and landscaping sections.
Construction
Measure square panels, slabs, plates, and other components used in building projects.
Education
Practice geometry, square numbers, square roots, perimeter, and the Pythagorean theorem.
Design and crafts
Calculate material requirements for square artwork, frames, fabric pieces, and decorative layouts.
Land measurement
Estimate the area of square plots and compare measurements in metric and imperial units.
Frequently asked questions
What is the formula for the area of a square?
The formula is A = s², where A is the area and s is the side length. Multiply the side length by itself. A square with a side length of 5 meters has an area of 25 m².
How do you calculate the perimeter of a square?
Use P = 4s. Multiply the side length by four because all four sides of a square are equal.
How do you find the diagonal of a square?
Use d = s√2. The diagonal forms a right triangle with two sides of the square, so the Pythagorean theorem gives this formula.
How do I find the side length if I know the area?
Take the positive square root of the area: s = √A. For example, if the area is 49 cm², the side length is 7 cm.
Can I calculate a square's area from its diagonal?
Yes. Use A = d² ÷ 2. Square the diagonal length and divide by two. Ensure that the diagonal is measured in a linear unit, and express the resulting area in the corresponding square unit.
Why is square area expressed in square units?
Area measures a two-dimensional surface. Multiplying a length by itself squares its unit, so meters produce square meters (m²) and feet produce square feet (ft²).
What is the difference between a square and a rectangle?
A square has four equal sides and four right angles. A rectangle also has four right angles, but only its opposite sides must be equal. A square is therefore a special type of rectangle.
Can I use this calculator with inches or feet?
Yes. Choose millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles for the side length, then choose your preferred area output unit.
Are my measurements uploaded or stored?
The calculations run locally in your browser using JavaScript. The calculator does not need to send your measurements to a server to perform the calculations.
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