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How to use
Use the rhombus calculator to find area, perimeter, height, side length and diagonals. You can start from the two diagonals or from a side length and interior angle. For rhombus diagonals of 16 cm and 12 cm, the area is 96 cm². Half-diagonals of 8 and 6 form a right triangle, giving a side of √(8² + 6²) = 10 cm, perimeter 40 cm and height 96 ÷ 10 = 9.6 cm.
- Choose diagonals or side-and-angle input.
- Enter positive values and choose a length unit.
- Review area, perimeter and the derived dimensions.
How it is calculated
Example
For diagonals 10 cm and 6 cm, area = 10×6÷2 = 30 cm² and side = ½√(10²+6²) ≈ 5.831 cm.
Important notes
In side-angle mode the angle must be strictly between 0° and 180°. Extremely large inputs that overflow browser number arithmetic are rejected rather than shown as an infinite result.
Worked examples and interpreting results
For a rhombus with diagonals 6 and 8, area is half their product. Its diagonals bisect one another at right angles, so half-diagonals 3 and 4 determine the side length.
| Case | Calculation | Result |
|---|---|---|
| Area | 6 × 8 ÷ 2 | 24 |
| Side length | √(3² + 4²) | 5 |
| Perimeter | 4 × 5 | 20 |
How to check the result
Do not omit the division by two when multiplying diagonals. If you start with a side and an angle, area depends on the sine of that angle. A square is a special rhombus with a 90-degree angle.
Rhombus area using diagonals and side length
The area of a rhombus equals the product of its diagonals divided by two, or base length multiplied by perpendicular height. Its perimeter is four times the side length.
- Area from diagonals 6 and 8: 6×8÷2 = 24
- Perimeter for side length 5: 4×5 = 20
- Area from base 5 and height 4: 5×4 = 20
Calculation caveat
The sloping side is not necessarily the perpendicular height. A rhombus has perpendicular diagonals, so the diagonal area formula applies.
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Frequently asked questions
How do I calculate the area of a rhombus?
Use A=d₁d₂/2 when both diagonals are known, or A=a²sin(θ) when side length and the included angle are known.
Are rhombus diagonals perpendicular?
Yes. They intersect at right angles and bisect each other.
Is a square a rhombus?
Yes. A square is a rhombus with right angles.
How is area found from side and angle?
Use A = a² sin(θ).
Are a rhombus’s diagonals always equal?
No. The diagonals of a rhombus are perpendicular and bisect each other, but they are generally different lengths. They are equal only in the special case where the rhombus is a square.
How do I find rhombus perimeter from diagonals?
Use P = 2√(d₁² + d₂²), because each side is half the square root of the sum of squared diagonals. Express both diagonals in the same unit.