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How to use
This tool handles a rectangle in two directions. With length and width it returns area, perimeter and diagonal. With area and perimeter it solves the two equations together and recovers the side lengths when the measurements are geometrically valid.
- Choose which measurements you know.
- Enter length and width, or enter area and perimeter.
- Calculate; the tool validates the geometry before solving.
- Review the two sides, area, perimeter, diagonal and side ratio.
How it is calculated
Example
Example: a rectangle 8 by 5 has area 40, perimeter 26 and diagonal √89 ≈ 9.434. In reverse mode, area 40 plus perimeter 26 recovers sides 8 and 5.
Important notes
Use one consistent length unit. Perimeter and diagonal use that same unit, while area uses the squared unit. Not every area/perimeter pair is possible; if the perimeter is too small for the stated area, no real rectangle exists.
Worked examples and interpreting results
Use a rectangle 8 units long and 5 units wide to calculate its area and perimeter.
| Case | Calculation | Result |
|---|---|---|
| Area | 8 × 5 | 40 |
| Perimeter | 2 × (8 + 5) | 26 |
How to check the result
Area uses squared units, while perimeter uses length units. A supplied area and perimeter must describe a feasible rectangle.
Frequently asked questions
Can a rectangle be solved from area and perimeter alone?
Yes, if the pair is geometrically valid. The result may be a square when both sides are equal.
Is the diagonal the same as a side?
No. It connects opposite corners and follows the Pythagorean theorem.
What if I swap length and width?
Area, perimeter and diagonal stay the same; only the side labels swap.