Area of a Rhombus

This calculator gives the area of a rhombus from the lengths of its two diagonals — the quickest route when the diagonals are known or easy to measure.

How the calculation works

It uses A = ½ × d₁ × d₂. The formula comes from the fact that a rhombus's diagonals cross at right angles and split it into four identical right triangles with legs d₁/2 and d₂/2. Adding up those triangles gives exactly half the product of the diagonals; put another way, the rhombus fills half of the rectangle drawn around it with sides d₁ and d₂.

Enter both diagonals in metres and the area comes out in square metres. The formula itself is unit-agnostic: if you type inches or feet, read the result as square inches or square feet. The order of the two diagonals does not matter.

Worked example

With the defaults d₁ = 8 m and d₂ = 6 m, A = ½ × 8 × 6 = 24 m². The side follows from the same right triangle: half-diagonals of 4 m and 3 m give a side of √(4² + 3²) = 5 m, so the perimeter is 4 × 5 = 20 m.

Things to keep in mind

• If you know the side a and the height h, the area is a × h; with the side and an interior angle α it is a² × sin α. Use those when the diagonals are not available.
• A square is a rhombus with equal diagonals, so with d₁ = d₂ = d the area is d² / 2 — a handy check.
• When you have measured the sides and both diagonals, verify that d₁² + d₂² = 4a². If it does not hold, one of the measurements is off or the shape is not a true rhombus.
• For tiles or flooring laid on the diagonal, add 10–15 % for cuts; diamond patterns waste more material than straight lay.