Rectangle
Find the sides, area, perimeter, diagonal and angle between the diagonals of a rectangle from two sides, a side and the diagonal, or the perimeter and area.
The rectangle calculator finds the sides, area, perimeter, diagonal, circumradius and the angle between the diagonals. A rectangle can be given by two sides, a side and the diagonal, a side and the area or the perimeter, the perimeter and the area, or the diagonal and the angle between the diagonals.
Rectangle formulas
| Value | Formula |
|---|---|
| Area | S = a · b |
| Perimeter | P = 2(a + b) |
| Diagonal | d = √(a² + b²) |
| Circumradius | R = d/2 |
| Area from the diagonals | S = ½ · d² · sin φ |
Example 1. Sides 8 cm and 6 cm.
S = 8 · 6 = 48 cm², P = 2 · (8 + 6) = 28 cm, d = √(64 + 36) = 10 cm.
How to find the sides from the perimeter and area
The sides a and b are the roots of the quadratic equation t² − (P/2)t + S = 0: their sum is the semiperimeter and their product is the area (Vieta's formulas).
Example 2. P = 28 cm, S = 48 cm².
t² − 14t + 48 = 0, D = 196 − 192 = 4, t = (14 ± 2)/2 ⇒ a = 8 cm, b = 6 cm.
Properties of a rectangle
- Opposite sides are equal and parallel, all angles are right angles.
- The diagonals are equal and bisect each other.
- Every rectangle has a circumscribed circle centered at the intersection of the diagonals.
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