Rhombus
Find the area, perimeter, diagonals, angles, height and inradius of a rhombus from a side and angle, the diagonals or a side and height.
What is known:
Side a
x
Angle α, °
x
Units:
Lengths are positive numbers (whole or decimal), angles are in degrees.
The rhombus calculator finds the area, perimeter, diagonals, angles, height and inradius of a rhombus. A rhombus can be given by a side and an angle, two diagonals, a side and the height, or a side and a diagonal.
Rhombus formulas
| Value | Formula |
|---|---|
| Area from the diagonals | S = d1 · d2 / 2 |
| Area from a side and an angle | S = a² · sin α |
| Area from a side and the height | S = a · h |
| Side from the diagonals | a = √(d1² + d2²) / 2 |
| Diagonals from a side and an angle | d1 = 2a sin(α/2), d2 = 2a cos(α/2) |
| Inradius | r = h / 2 |
Example. The diagonals of a rhombus are 6 cm and 8 cm.
S = 6 · 8 / 2 = 24 cm², a = √(9 + 16) = 5 cm, P = 20 cm, h = 24 / 5 = 4.8 cm.
Properties of a rhombus
- All sides are equal, opposite angles are equal.
- The diagonals are perpendicular, bisect each other and bisect the angles.
- Every rhombus has an inscribed circle centered at the intersection of the diagonals.
- A rhombus with right angles is a square.
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