Diagonal of a Square Calculator

How to Calculate the Diagonal of a Square

A square's diagonal is the straight line connecting two opposite corners. Because all four angles in a square are right angles, drawing a diagonal splits the square into two identical right-angled triangles. Each triangle has the two sides of the square as its legs and the diagonal as its hypotenuse. Applying Pythagoras's theorem (a squared plus b squared equals c squared) with both legs equal to the side length s gives d squared = s squared + s squared = 2s squared, so d = s times the square root of 2.

Worked Example

Take a square with a side length of 5 units. The diagonal is 5 × 1.414214 = 7.071068, which rounds to 7.07 units. The area is 5² = 25 square units, and the perimeter is 4 × 5 = 20 units.

Working Backwards from the Diagonal

If you already know the diagonal and need the side length, divide by the square root of 2 (or multiply by 0.707107). For example, a square with a diagonal of 10 units has a side length of 10 ÷ 1.414214 = 7.071068 units, which rounds to 7.07 units.

Where This Comes Up

Finding a square's diagonal is common in building and trades work, such as checking that a foundation, deck, or room frame is square by comparing the two diagonal measurements (they should be equal). It also comes up in packaging (fitting a square item into a round tube), screen and display sizing, and general geometry problems in maths and stats.

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Sources: Standard Euclidean geometry and Pythagoras's theorem, as taught in the NZ maths curriculum (nzmaths.co.nz). The diagonal to side ratio (√2 ≈ 1.41421) is a fixed mathematical constant.

This calculator gives exact results for a perfect square based on the values you enter. Rounding is applied for display only; the underlying calculation uses full precision.