How this calculator works
A square is a rectangle with four equal sides and four right angles. Every measurement is tied to the side length, so knowing any one of the four values recovers the rest. The area is the side squared, the perimeter is four times the side, and the diagonal comes from the Pythagorean theorem applied to a right triangle with two equal legs. This calculator accepts the value you know, finds the side, and reports all four properties in the length and area units you choose.
Formula
Side s. Area = s². Perimeter = 4s. Diagonal = s√2. Therefore s = √A, s = P/4, and s = d/√2.
Worked example
A square with side 5 m has area 25 m², perimeter 20 m and diagonal 5√2 ≈ 7.0711 m. A square with diagonal 10 m has side 10/√2 ≈ 7.0711 m and area 50 m².
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Frequently asked questions
Why is the diagonal √2 times the side?
The diagonal splits the square into two right triangles with equal legs. The Pythagorean theorem gives diagonal² = s² + s², so diagonal = s√2.
What is the difference between this and the square area calculator?
The square area calculator starts from the side only. This one can also start from the area, perimeter or diagonal and then reports every property.
Can the diagonal be shorter than the side?
No. The diagonal is always the longest distance inside a square, about 1.414 times the side. The calculator derives a valid side from any positive diagonal you enter.
Does doubling the side double the area?
No. Doubling the side multiplies the area by four, because area depends on the square of the side. The perimeter only doubles.