Square calculator
Area, perimeter and diagonal of a square from any one of them.
Fill in the fields and the result will appear here automatically.
Solves a square from whichever value you happen to have: the side, the area or the perimeter. All four quantities come back together, so a floor area of 49 m² immediately tells you the 7 m wall it runs along and the 9.9 m diagonal you would measure across it. The length unit is chosen once and never converted — the area is simply reported in its square.
How it works
Formula and logic
S = a², P = 4a and d = a√2. In inverse modes a = √S or a = P/4, then the other dimensions follow. Area uses the square of the selected length unit.
Example
A square room with a 5 m side has an area of 25 m², a perimeter of 20 m and a diagonal of 7.071 m.
Fields and units
- Length unit — list option
- What is known — list option
- Side — cm
- Area — cm²
- Perimeter — cm
How to use
- — Choose the square’s side, area or perimeter as the known value.
- — Lengths use the selected unit and area uses its square.
- — Enter a positive value.
- — To change cm² to m², divide the area by 10,000 before entering it; selecting metres alone does not convert it.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: area, perimeter and squared units OpenStax: Pythagorean theorem for a right triangle
- Limitation
- The model assumes four equal sides and four right angles. Area alone does not prove that a plot is square. Results are rounded; a degenerate square with a zero side is outside this calculator’s scope.
FAQ
Can I enter the area instead of the side?
Yes. Choose the area mode and the side is recovered as its square root, then the perimeter and diagonal follow from it.
Why is the area shown in squared units?
Because that is what an area is. If you entered centimetres, the area is in square centimetres — multiplying by a linear factor to change unit would be wrong.
Is a zero side accepted?
No. A square with no side is not a figure, so the calculator reports the problem instead of returning a plausible zero.
How is the diagonal found?
By the Pythagorean theorem across two equal sides, which reduces to d = a√2.
What changes when I double a square’s side?
Perimeter and diagonal double, while area becomes four times as large: (2a)² = 4a². A factor applied to length therefore has a different effect on area.