A 5 m by 3 m floor has area 5 × 3 = 15 m², perimeter 2 × (5 + 3) = 16 m, and diagonal √(5² + 3²) = 5.83 m.
A 20 m² plot with a 4 m width has length 20 m² ÷ 4 m = 5 m. Its fence line is 2 × (5 + 4) = 18 m.
A panel with a 13 in diagonal and 5 in side has the other side √(13² − 5²) = 12 in, so it needs a 12 in by 5 in opening.
Let L be one side, W the other side, A area, P perimeter, d diagonal and R circumradius. Results label the longer solved side as length and the shorter as width; rotating a rectangle swaps the side directions without changing its properties.
| What you know | What you need | Formula | Validity condition |
|---|---|---|---|
| Length L and width W | Area | A = L × W | L > 0 and W > 0 |
| Length L and width W | Perimeter | P = 2(L + W) | L > 0 and W > 0 |
| Length L and width W | Diagonal | d = √(L² + W²) | L > 0 and W > 0 |
| Area A and width W | Length | L = A ÷ W | A > 0 and W > 0 |
| Diagonal d and one side W | Other side | L = √(d² − W²) | d > W > 0 |
| What you know | What you need | Formula | Validity condition |
|---|---|---|---|
| Perimeter P and area A | Both sides | S = P/2; L,W = (S ± √(S² − 4A))/2 | 0 < A ≤ P²/16 |
| Perimeter P and diagonal d | Both sides | A = ((P/2)² − d²)/2, then use P and A | P/(2√2) ≤ d < P/2 |
| Diagonal d and area A | Both sides | S = √(d² + 2A); solve t² − St + A = 0 | 0 < A ≤ d²/2 |
| Diagonal d | Circumradius | R = d/2 | d and R are dependent, so together they do not determine the sides |
Circle and diagonal accuracy: a rectangle’s equal diagonals bisect each other, but equal diagonals alone do not prove that an arbitrary quadrilateral has right angles. Every rectangle has a circumscribed circle with radius d/2. A general rectangle does not have an incircle tangent to all four sides unless it is a square; this calculator instead reports the radius of the largest circle that fits inside, equal to half the shorter side.
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Starlight Tools editorial team
Mathematical review:
Elementary Euclidean geometry, Pythagorean and quadratic formulas
Numerical policy:
Calculations use full browser precision. Extra values agree when their difference is within a relative tolerance of 1 × 10−9, with a 1 × 10−12 absolute floor. Rounding is applied only for display.
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For length L and width W, area is L × W, perimeter is 2 × (L + W), and diagonal is √(L² + W²). For a 5 m by 3 m rectangle, the area is 15 m², the perimeter is 16 m, and the diagonal is approximately 5.83 m.
Divide the area by the width: L = A ÷ W. If the area is 20 m² and the width is 4 m, the length is 20 m² ÷ 4 m = 5 m.
No. Rectangles can have the same area but different side lengths and perimeters. An area of 24 m² could be 6 m by 4 m with a 20 m perimeter, or 8 m by 3 m with a 22 m perimeter.
No. Many rectangles can share one diagonal length. You also need a side, the area, or the perimeter. Diagonal and circumradius are dependent because the circumradius is always half the diagonal, so that pair does not uniquely define a rectangle.
Length, width, diagonal and perimeter use linear units, while area uses square units. If length and width are entered in metres, area is in square metres (m²). Convert all entered lengths to the same selected unit before calculating.
A rectangle has four right angles and opposite sides equal. A square is a special rectangle whose four sides are all equal. Every square is a rectangle, but not every rectangle is a square.
