Area of a Rhombus Calculator
Calculate the area, side length, and perimeter of a rhombus from its two diagonals. See also Area of Parallelogram Calculator and Area of Rectangle Calculator.
How to Calculate the Area of a Rhombus
A rhombus is a quadrilateral with all four sides equal. Its diagonals bisect each other at right angles. To find the area, multiply the two diagonals and divide by 2. The side length can be found from the diagonals using the Pythagorean theorem: side = √((d₁/2)² + (d₂/2)²), since each half-diagonal forms a right triangle with the side.
Rhombus Area Formula
A = ½ × d₁ × d₂
Side = √((d₁/2)² + (d₂/2)²)
Perimeter = 4 × side
Example
Find the area of a rhombus with diagonals 10 and 8:
A = ½ × d₁ × d₂
A = ½ × 10 × 8
A = 40 square units
Side = √(5² + 4²) = √(25 + 16) = √41 ≈ 6.4031
Perimeter = 4 × 6.4031 ≈ 25.6125
Rhombus Area Reference Table
| d₁ | d₂ | Area | Side | Perimeter |
|---|---|---|---|---|
| 4 | 3 | 6.00 | 2.5000 | 10.0000 |
| 6 | 4 | 12.00 | 3.6056 | 14.4222 |
| 8 | 6 | 24.00 | 5.0000 | 20.0000 |
| 10 | 8 | 40.00 | 6.4031 | 25.6125 |
| 12 | 8 | 48.00 | 7.2111 | 28.8444 |
| 14 | 10 | 70.00 | 8.6023 | 34.4093 |
| 16 | 12 | 96.00 | 10.0000 | 40.0000 |
| 20 | 14 | 140.00 | 12.2066 | 48.8262 |
| 24 | 18 | 216.00 | 15.0000 | 60.0000 |
| 30 | 20 | 300.00 | 18.0278 | 72.1110 |
Frequently Asked Questions
What is a rhombus?
A rhombus is a quadrilateral with all four sides of equal length. It is a special type of parallelogram. Its diagonals bisect each other at right angles (90°).
Is a square a rhombus?
Yes. A square is a special rhombus where all angles are 90°. In a square, the two diagonals are equal in length. The area formula A = ½d₁d₂ still applies.
How do I find the diagonals if I know the side and an angle?
If you know side s and angle θ: d₁ = 2s × sin(θ/2) and d₂ = 2s × cos(θ/2). Then use A = ½d₁d₂ or equivalently A = s² × sin(θ).
What is the relationship between the diagonals?
The diagonals of a rhombus always bisect each other at right angles. They also bisect the vertex angles. The longer diagonal connects the vertices with the smaller angles.