Everyday utility

Square Calculator

Enter the side length to instantly get area, perimeter, diagonal, and inscribed circle radius. All four sides of a square are equal, so one number describes the whole shape.

Last reviewed May 19, 2026 by ToolSpilo Editorial Team.

Review method: Reviewed against standard square geometry formulas and Pythagorean theorem derivation.

Calculator tool

How this calculator works

Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.

What Makes a Square Special

A square is a rectangle where all four sides are equal and every corner is 90°. Because of this symmetry, one measurement — the side length — determines every other property of the shape.

Formulas

Let ss be the side length.

MeasurementFormulaFor s=5s = 5
AreaA=s2A = s^225 sq units
PerimeterP=4sP = 4s20 units
Diagonald=s2d = s\sqrt{2}≈ 7.07 units
Inscribed circle radiusr=s/2r = s/22.5 units

Worked Example

For a square with side 5 m:

A=52=25 m2A = 5^2 = 25\text{ m}^2
d=52≈7.07 md = 5\sqrt{2} \approx 7.07\text{ m}

The diagonal is always longer than the side by a factor of 2≈1.414\sqrt{2} \approx 1.414.

The Diagonal Formula Explained

The diagonal splits the square into two right isosceles triangles. Both legs are equal to ss, so by the Pythagorean theorem:

d=s2+s2=2s2=s2d = \sqrt{s^2 + s^2} = \sqrt{2s^2} = s\sqrt{2}

Practical Uses

Square calculations appear in room layouts (square tiles, flooring), garden beds, cutting materials, fabric squares, display stands, and architectural plans. The inscribed circle radius tells you the largest circle that fits inside the square without overlap.

Frequently asked questions

Why is the area of a square $s^2$ and not $4s$?

Area measures the surface inside the shape, not the boundary. 4s4s is the perimeter — the total distance around the outside. Area uses squared units because it covers two dimensions: length and width. For a square, both equal ss, so the area is s×s=s2s \times s = s^2.

What is the diagonal of a square used for in practice?

The diagonal is the longest straight line inside a square. It appears when checking if a square piece of material fits inside a circular frame, when laying square tiles diagonally across a floor, and when builders verify right angles by measuring corner-to-corner. A room with two equal diagonals has perfectly square corners.

What is the inscribed circle radius of a square?

The inscribed circle is the largest circle that fits inside the square and touches all four sides. Its radius is half the side length: r=s/2r = s/2. For a square with side 10 m, the inscribed circle has radius 5 m and area π×52≈78.54 m2\pi \times 5^2 \approx 78.54\text{ m}^2. This matters in machinery design, packaging, and any problem involving a circle fitted inside a square frame.

How do I convert between a square's area and its side length?

Area and side are related by A=s2A = s^2, so s=As = \sqrt{A}. If a square room has area 36 m², the side is 36=6 m\sqrt{36} = 6\text{ m}. This works in reverse: enter the side to get area, or use the square root of area to find the side.