Rhombus Area Calculator
Calculate the area of a rhombus from its major and minor diagonals. Formula: A = (D × d) / 2.
Formula
A = (D × d) / 2
Area of a rhombus
All four sides of a rhombus are equal, and its two diagonals cut each other in half at a right angle. Once you have the major diagonal D and the minor diagonal d, the area follows from A = (D·d)/2. Take D = 8 m and d = 6 m and you get A = (8·6)/2 = 24 m². When the diagonals aren't handy but you do know the side L and an interior angle α, there's a second route: A = L²·sen(α).
Since the sides are all the same length, the perimeter is just P = 4·L. A square is a special rhombus where α = 90°, which also makes D = d. And no matter the shape, the diagonals cross at 90° and carve the rhombus into four congruent right triangles.
Applications
You'll spot rhombi in traditional kites (the diamond kite), in crystallography, where a number of minerals crystallise into rhombic faces, and in the argyle pattern on socks and sweaters. Heraldry uses them too. The central rhombus on the Brazilian flag follows a 7:9 proportion that José Bonifácio picked so the green field would keep a clean border all around it.
FAQ
Is every square a rhombus? Yes. A square is just a rhombus whose four interior angles all happen to be 90°. The reverse isn't true, though: most rhombi aren't squares.
How do I find the side from the diagonals? The diagonals are perpendicular and split each other in half, so each half-diagonal is a leg of a right triangle: L = √((D/2)² + (d/2)²). With D = 8 and d = 6 that gives L = √(16+9) = 5 m.
What is the relation between a rhombus and a parallelogram? A rhombus is a parallelogram that happens to have all four sides equal. Opposite sides stay parallel and opposite angles stay equal, exactly as in any parallelogram.
Why are the diagonals always perpendicular? Each diagonal doubles as an axis of symmetry. Reflecting the rhombus across one of them has to land it back on itself, and the only way that works is if the other diagonal sits at 90°.
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Calculate the area of a rhombus
Trying to solve it from the sides is where people slip. A rhombus's area comes from its two diagonals, and that mix-up is the most common one. Here the math follows A = (D × d) / 2, using the major and minor diagonals, and the number shows up as you type.
It works for geometry exercises, for finding the area of a kite, of a rhombus in a design project or of a part shaped that way. You pass the two diagonals, the tool solves it, and there's no way to fall into the trap of multiplying the sides.
Nothing leaves your browser; the calculation happens right there. A direct reference for a rhombus's area with the correct formula, the diagonal-based one.