How do you calculate the area of a square?

Area of a square = side x side = s^2. Example: a square with side length 9 cm has area = 9^2 = 81 cm^2. Area is always expressed in square units. If you know the diagonal instead of the side, use: area = d^2 / 2, where d is the diagonal length.

How do you find the diagonal of a square?

The diagonal of a square = side x sqrt(2). This comes from the Pythagorean theorem applied to the two equal sides. Example: a square with side 5 cm has diagonal = 5 x sqrt(2) = 5 x 1.4142 = 7.07 cm. The diagonal is always approximately 1.414 times the side length.

What is the perimeter of a square?

Perimeter = 4 x side (since all four sides of a square are equal). Example: a square with side 6 m has perimeter = 4 x 6 = 24 m. If you know the area and need the perimeter: side = sqrt(area), then perimeter = 4 x sqrt(area). If you know the diagonal: side = diagonal / sqrt(2), then perimeter = 4 x side.

What is the difference between a square and a rhombus?

A square and a rhombus both have four equal sides. The difference is angles: a square has four right angles (90 degrees each), while a rhombus can have any angle. A square is therefore a special rhombus with right angles. A rhombus is also called a diamond shape in everyday language. The area formula differs: square area = s^2, rhombus area = (d1 x d2) / 2 where d1 and d2 are the diagonals.

How do you find the side of a square from its area?

Side = sqrt(area). If the area of a square is 64 m^2, then side = sqrt(64) = 8 m. If the area is not a perfect square, use a calculator: area = 50 m^2 gives side = sqrt(50) = 7.07 m. You can verify: 7.07^2 = 49.98, which rounds to 50.

Square Calculator

Calculate area, perimeter, and diagonal of a square. Supports cm, m, ft, and inches.

🟦 What is a Square?

A square is a regular quadrilateral - a flat, two-dimensional shape with four equal sides and four right angles (90° each). Because all sides are identical and all angles are right angles, a square is simultaneously a special case of a rectangle (all angles 90°), a rhombus (all sides equal), and a parallelogram (opposite sides parallel).

Squares appear everywhere in everyday life - floor tiles, chessboards, window panes, pixels on a screen, and countless engineering applications. Understanding how to calculate the area, perimeter, and diagonal of a square is one of the most fundamental skills in geometry.

The three key measurements of a square all derive from a single value: the side length. Once you know the side, every other property of the square is fully determined. This calculator computes all three instantly in your chosen unit.

📐 Square Formulas

Area = s²

Perimeter = 4s

Diagonal = s × √2

s = Side length (any unit)

Area = in square units (e.g. cm², m²)

Perimeter = total boundary length in same units as s

Diagonal = distance between opposite corners = s × 1.41421...

The diagonal formula comes directly from the Pythagorean theorem. Since a diagonal cuts the square into two right-angled triangles with legs s and s, the hypotenuse (diagonal) = √(s² + s²) = √(2s²) = s√2.

Area is measured in square units - if s is in centimetres, area is in cm². If s is in metres, area is in m². The calculator handles this automatically based on your selected unit.

📖 How to Use This Calculator

Steps

Select your unit using the tabs (cm, m, ft, or in). The result labels update accordingly.

Enter the side length by typing it in or dragging the slider.

Click Calculate to see area, perimeter, and diagonal instantly.

💡 Example Calculations

Example 1 - Floor Tile (10 cm side)

Side = 10 cm

Area = 10² = 100 cm²

Perimeter = 4 × 10 = 40 cm

Diagonal = 10 × √2 = 10 × 1.41421 = 14.142 cm

Try this example →

Example 2 - Large Room (5 m side)

Side = 5 m

Area = 5² = 25 m²

Perimeter = 4 × 5 = 20 m

Diagonal = 5 × 1.41421 = 7.071 m

Try this example →

❓ Frequently Asked Questions

How do I find the side of a square if I know the area?+

Take the square root of the area. If Area = 64 cm², then side = √64 = 8 cm. You can also enter a reverse calculation: if you know the area you want, the side length needed is √Area.

How do you find the side length of a square given the area?+

Side = sqrt(Area). If the area is 64 sq cm, side = sqrt(64) = 8 cm. This is why square roots are named as they are - finding the square root of an area gives you the side of a square with that area. For non-perfect-square areas, use a calculator: sqrt(50) = 7.071 cm.

What is the inscribed circle radius of a square?+

The inscribed circle (incircle) has radius r = side / 2. It touches all four sides of the square. The circumscribed circle (circumcircle) passes through all four corners and has radius R = side x sqrt(2) / 2 = diagonal / 2. For a 10 cm square, incircle radius = 5 cm and circumcircle radius = 7.07 cm.

What is the relationship between a square side and its diagonal?+

Diagonal = side x sqrt(2) which is approximately side x 1.414. This comes from the Pythagorean theorem: both legs of the right triangle formed by the diagonal are equal to the side. For a 7 cm square, diagonal = 7 x 1.414 = 9.9 cm. Conversely, side = diagonal / sqrt(2).

What is the relationship between a square's diagonal and its side?+

The diagonal is always the side length multiplied by √2 (approximately 1.41421). Conversely, if you know the diagonal d, the side = d / √2 = d × 0.7071. This relationship comes from the Pythagorean theorem applied to the right triangle formed by two sides and a diagonal.

How many tiles of a given size fit in a square room?+

Divide the room area by the tile area. For example, a 5 m × 5 m room has area 25 m² = 250,000 cm². A 30 cm × 30 cm tile has area 900 cm². Number of tiles = 250,000 / 900 ≈ 278 tiles. Always add 10–15% extra for cuts and waste.

Is a square a rectangle? Is a square a rhombus?+

Yes to both. A rectangle requires all angles to be 90° - a square satisfies this. A rhombus requires all sides to be equal - a square satisfies this too. So a square is a special case of both a rectangle and a rhombus. It is also a parallelogram and a kite.

What is the formula for the area of a square?+

Area of a square = side^2 (side length squared). Perimeter = 4 x side. Diagonal = side x sqrt(2). Example: a square with side 5 cm has area 25 cm^2, perimeter 20 cm, and diagonal 5 x 1.414 = 7.07 cm. The square is a special case of a rectangle (all sides equal) and a rhombus (all angles 90 degrees).

How do I find the side of a square given its area?+

Side = sqrt(Area). For area 144 cm^2, side = sqrt(144) = 12 cm. For a non-perfect square area like 50 cm^2, side = sqrt(50) = 7.071 cm. This is equivalent to finding the square root of the area. The calculator handles this automatically - enter the area and it calculates the side length.

How is a square different from a rhombus and rectangle?+

A square has all four sides equal AND all four angles equal (90 degrees). A rhombus has all sides equal but angles need not be 90 degrees. A rectangle has all angles 90 degrees but sides can be unequal. A square is both a special rectangle and a special rhombus. All squares are rectangles and rhombuses, but not vice versa.

What are real-world uses of square area calculations?+

Square area calculations are used in flooring (tiles, carpeting), framing (picture frames, wall tiles), land measurement (square plots), material estimation (paint, fabric), and physics (cross-sectional area of wires, resistivity). Engineers use square cross-sections for structural columns and beams. Architects use them for room planning and building footprints.