Square Diagonal Calculator

What is a square diagonal calculator?

A square diagonal calculator finds the length of the straight line that joins two opposite corners of a square. Because all four sides of a square are equal and every corner is a right angle, the diagonal is tied to the side length by a single fixed ratio. The tool works in both directions: enter the side to get the diagonal, or enter the diagonal to recover the side. When you start from the side it also reports the area and perimeter of the square.

Key concepts

• Side (s) — the length of one edge of the square; all four edges share this length.
• Diagonal (d) — the distance between two opposite corners, cutting the square into two right triangles.
• Area (A) — the surface enclosed by the square, equal to the side squared.
• Perimeter (P) — the total distance around the square, equal to four times the side.

How does the calculator work?

The diagonal of a square is the hypotenuse of a right triangle whose two legs are sides of the square. Applying the Pythagorean theorem with both legs equal to $s$ gives a diagonal of $s\sqrt{2}$. The calculator converts your input to a common internal unit, applies the formula, and converts the result back to whichever unit you select.

Formulas

Diagonal from side:

Side from diagonal:

Area and perimeter:

Worked examples

Example 1: diagonal, area and perimeter from a side

A square has a side of 5 cm. Its diagonal is:

The area is $A = 5^2 = 25 \text{ cm}^2$ and the perimeter is $P = 4 \cdot 5 = 20 \text{ cm}$.

Example 2: a larger square

For a side of 10 cm:

Example 3: side from diagonal

A square has a diagonal of 7.0711 cm. Its side is:

Practical uses

• Carpentry and construction — checking that a frame is truly square by measuring its diagonals, which must be equal.
• Tiling and flooring — laying tiles on the diagonal or fitting square pieces into a space.
• Screen and display sizing — relating the diagonal measurement of a square panel to its side.
• Design and layout — sizing square photos, labels, or signage from a corner-to-corner measurement.

Notes

• The side and the diagonal must be positive for the result to be meaningful; a value of 0 collapses the square to a point.
• The diagonal is always longer than the side by the irrational factor $\sqrt{2} \approx 1.41421$.
• The units of the side and the diagonal match: a side in metres gives a diagonal in metres. Switching the unit selector reconverts the result automatically.
• For a non-square rectangle the two sides differ, so use the diagonal of rectangle calculator instead. To work with circles, see the circle area calculator.