Area of a Square

One measurement is enough: the calculator squares the side and also returns the perimeter and the diagonal of the square.

How the calculation works

A square has four equal sides and four right angles, so its area is the side multiplied by itself: A = s × s = s². That is literally where the word “squared” comes from. If the side is in metres, the area is in square metres.

Alongside the area you get the perimeter, P = 4s, and the diagonal, d = s√2 ≈ 1.4142 × s. The diagonal follows from the Pythagorean theorem (d² = s² + s² = 2s²) and is useful for checking a layout for square corners or seeing whether a square panel will fit through an opening.

There is a single input, side a, labelled in metres; decimals are allowed. Any unit works as long as you read the answer in the matching square unit: feet give square feet, inches give square inches.

Worked example

The default side is 5 m. Area = 5² = 25 m², perimeter = 4 × 5 = 20 m, diagonal = 5 × √2 ≈ 7.0711 m. Compare a 6 × 4 m rectangle: same 20 m perimeter, but only 24 m² of area — for a fixed perimeter, the square encloses the most area of any rectangle.

Things to keep in mind

• Doubling the side quadruples the area: a 10 ft square is 100 sq ft, not 50.
• A 12 × 12 inch tile covers exactly 1 sq ft, so a 10 × 10 ft floor needs 100 tiles before cut waste (typically add 5–10%).
• The side field accepts up to 100. For a square lot 150 m on a side, enter 15 and multiply the result by 100: 22,500 m².
• To get the side from a known area, take the square root: 36 m² means a 6 m side.