Square Calculator

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

🟦 Square Calculator
Side Length 10 cm
cm
01000
Area
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Perimeter
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Diagonal
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🟦 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

1
Select your unit using the tabs (cm, m, ft, or in). The result labels update accordingly.
2
Enter the side length by typing it in or dragging the slider.
3
Click Calculate to see area, perimeter, and diagonal instantly.

💡 Example Calculations

Example 1 - Floor Tile (10 cm side)

Side = 10 cm

1
Area = 10² = 100 cm²
2
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

1
Area = 5² = 25 m²
2
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.
Tags: Square Area Perimeter Diagonal Geometry 2d Shape Calculator

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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.

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).

📌 Quick Tips

💡The diagonal of a square is always side × √2 ≈ side × 1.414.
💡Area scales with the square of the side - doubling the side quadruples the area.
💡All four sides and all four angles (90°) of a square are equal - it is both a rectangle and a rhombus.
💡Use this calculator as a starting point, then consult a professional for high-stakes decisions.
💡Share the URL after calculating — the address bar updates with your inputs for easy sharing.