A rhombus (sometimes called a diamond shape) is a quadrilateral with four equal sides. Because the sides are equal but the angles need not be 90°, a rhombus is more general than a square and is a special case of a parallelogram. This calculator finds the area of a rhombus from whichever measurements you have, shows the full arithmetic working, and can even back-solve a missing diagonal when you already know the area.
Three ways to calculate rhombus area
Method 1 — From the two diagonals
Every rhombus has two diagonals that cross at right angles and bisect each other. If the diagonals are p and q:
Area = (p x q) / 2
This is the most common formula in geometry textbooks. For example, if p = 10 and q = 6 then the area is (10 x 6) / 2 = 30 square units.
Method 2 — From side and height
The height h is the perpendicular distance between two parallel sides:
Area = side x height
This is analogous to the rectangle formula and is easiest to use when the altitude is physically measurable (e.g. on a tiled floor).
Method 3 — From side and an interior angle
When you know one side length a and one interior angle theta (in degrees):
Area = a(squared) x sin(theta)
The sine term accounts for how “tilted” the rhombus is. A 90° angle gives a square (sin 90° = 1), and the area is maximised at that point. For any other angle the area is smaller — a very flat or very tall rhombus with the same side length has a smaller enclosed area.
Worked example
A rhombus has diagonals of 12 cm and 8 cm. Find its area, side length, and perimeter.
- Area = (12 x 8) / 2 = 96 / 2 = 48 cm²
- Side = sqrt((12/2)² + (8/2)²) = sqrt(36 + 16) = sqrt(52) ≈ 7.211 cm
- Perimeter = 4 x 7.211 ≈ 28.84 cm
The SVG diagram in the tool labels p/2 and q/2 on the half-diagonals so you can visualise how the right-angle triangles fit together.
| Diagonal p | Diagonal q | Area | Side |
|---|---|---|---|
| 10 | 6 | 30 | 5.831 |
| 12 | 8 | 48 | 7.211 |
| 20 | 15 | 150 | 12.5 |
| 8 | 8 | 32 | 5.657 |
Formula notes
The diagonal formula follows directly from geometry: the diagonals cut the rhombus into four congruent right triangles, each with legs p/2 and q/2. The area of one such triangle is (1/2)(p/2)(q/2) = pq/8, and four of them gives pq/2.
The side-angle formula uses the fact that a rhombus can be constructed by placing two congruent isosceles triangles back-to-back. The area of each triangle is (1/2) x a x a x sin(theta), and two of them gives a(squared) x sin(theta).
All three formulas are equivalent — enter the same rhombus in any of the three modes and you will get the same area value, just reached by a different path.
Every calculation runs entirely in your browser. No measurements are uploaded or stored anywhere.