Rhombus calculator
Area, side, perimeter and height of a rhombus from its two diagonals.
Fill in the fields and the result will appear here automatically.
Calculates a rhombus’s area, side, perimeter and height from its two complete diagonals. The diagonals of a rhombus cross at right angles and bisect each other, so the side is the hypotenuse of a right triangle with legs d₁/2 and d₂/2, and the area is half their product. The height follows from the area as h = S/a, with no need to know any angle. A rhombus with equal diagonals is a square, and the calculator handles that case without special-casing.
How it works
Formula and logic
Area S = d₁·d₂/2. The side a = √((d₁/2)² + (d₂/2)²), because the diagonals bisect each other at right angles. Perimeter P = 4a and height h = S/a.
Example
A rhombus with diagonals of 6 and 8 cm has an area of 24 cm², a side of 5 cm and a height of 4.8 cm.
Fields and units
- Length unit — list option
- Diagonal d₁ — cm
- Diagonal d₂ — cm
How to use
- — Check that the figure is a rhombus with four equal sides.
- — Enter the full lengths of both diagonals, not their halves, in one unit.
- — The area uses that unit squared.
- — Compare height with side length: height is no greater than the side and equals it for a square.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: Pythagorean theorem for a right triangle
- Limitation
- Diagonals are assumed perpendicular and to bisect each other, as they do in a rhombus. Two diagonal lengths do not determine an arbitrary quadrilateral this way. All dimensions must be positive; results are rounded.
FAQ
Why is the area half the product of the diagonals?
The diagonals cut the rhombus into four right triangles with legs d₁/2 and d₂/2. Their combined area comes to d₁·d₂/2.
How does a rhombus differ from a parallelogram?
A rhombus is a parallelogram with four equal sides. Every parallelogram has equal opposite sides, but adjacent sides may differ. Two diagonal lengths determine a rhombus up to position; a general parallelogram needs the angle between its diagonals or other information as well.
What if the diagonals are equal?
You get a square — a rhombus with right angles. The calculation does not change: the side works out to d/√2 and the height equals the side.
Can I use a side and an angle instead?
Mathematically yes, but this calculator wants diagonals. In practice they are easier to obtain: an angle needs a protractor, a diagonal only a ruler.
Why is the height smaller than the side?
The height is the distance between two parallel sides, while the side itself runs at a slant. They would coincide only for a square standing on its side, that is at a right angle.
Are perpendicular diagonals enough for every rhombus formula?
No. They must also bisect each other and all four sides must be equal. Another quadrilateral with perpendicular diagonals may have the same area formula, but √((d₁/2)²+(d₂/2)²) for its side and 4a for its perimeter are not generally valid.