Square properties from any one value — side, area, perimeter or diagonal.
Any one property of a square determines all the others — pick whichever one you actually measured.
Area (square units)
From sideHow to use this tool
Pick what you actually know — side, area, perimeter or diagonal. The input label changes to match, so there is no guessing which box means what.
Enter the one value. It must be positive; a square with side zero has no area, perimeter or diagonal worth computing.
Side, area, perimeter and diagonal are all shown, plus the inradius (side ÷ 2) and circumradius (side ÷ √2) for geometry work.
Try a reverse route as a check: area 25, perimeter 20 and diagonal 7.0711 must all give side 5. If they do not, one of the measurements is off.
Formula & worked example
Worked example: a square of side 5 has area 5² = 25, perimeter 4 × 5 = 20 and diagonal 5√2 ≈ 7.0711. In reverse: an area of 25 gives side √25 = 5; a perimeter of 20 gives side 20 ÷ 4 = 5; and a diagonal of 7.0711 gives side 7.0711 ÷ √2 = 5 — every route lands on the same square.
Limitations — read this before you rely on it
This calculator is for squares only — four equal sides and four right angles. For rectangles, use the area calculator with separate length and width; for other quadrilaterals the formulas here do not apply. All properties share one unit system: enter the side in metres and the area comes out in square metres, the diagonal in metres.
Frequently asked questions
A square calculator finds every property of a square — area, perimeter and diagonal — from whichever one you know. Start from the side, or work backwards from the area, the perimeter or the diagonal; any one of them determines the whole square.
Area of a square = side × side. For side 5: 5 × 5 = 25 square units. If you know the area instead, the side is its square root: √25 = 5.
Diagonal = side × √2. For side 5: 5 × 1.4142 = 7.0711. That is Pythagoras on the two sides that meet at a corner: diagonal = √(side² + side²) = side√2.
Divide by 4: side = perimeter ÷ 4. A perimeter of 20 means side 5, area 25 and diagonal 7.0711. This is the reverse mode of the calculator — pick Perimeter and enter 20.
Yes — a square is a perfect square in the number sense too: its area is always a whole-number side squared (25, 36, 49 …). But the calculator works for any side, whole or not; a side of 5.5 gives area 30.25.