Rhombus Area Calculator

A rhombus has four equal sides. Every rhombus is a parallelogram, but not every parallelogram is a rhombus. The diagonals of a rhombus always meet at 90° and bisect each other — a useful identifier when you’re trying to figure out what shape you’re looking at.

Area from the two diagonals d₁ and d₂:

A = ½ × d₁ × d₂

Why divide by two? The two diagonals split the rhombus into four right triangles, each with legs d₁/2 and d₂/2. Each triangle has area (d₁/2)(d₂/2)/2 = d₁d₂/8. Four triangles total: 4 × d₁d₂/8 = d₁d₂/2.

Alternative formula if you know the side length s and one interior angle θ:

A = s² × sin(θ)

For a square (rhombus with 90° angles), sin(90°) = 1, so A = s². For other angles the area is smaller — a “flat” rhombus that’s almost folded has area near zero even with the same side length.

Where rhombuses show up in real measurements:

• Harlequin diamond tile patterns. Each diamond is a rhombus, usually with diagonals in a 2:1 ratio.
• Diamond playing-card pip. Just decorative, but the basic rhombus shape.
• Kite-shaped traffic warning signs in some countries (although those are technically kites, not rhombuses — see the kite-area calculator).
• Crystal habits. Quartz, calcite, and many minerals form rhombic crystal faces. Mineralogists measure diagonals to compute face area.
• Argyle pattern on socks and sweaters. Classic rhombic geometry.

Worked example — diamond pattern floor tile:

You’re laying a harlequin tile floor in 12 in × 6 in diamonds (these are the diagonals, not the side lengths). Area per tile = 0.5 × 12 × 6 = 36 sq in = 0.25 sq ft. For a 100 sq ft floor: 100 / 0.25 = 400 tiles. Add 10% waste = 440 tiles.

Side length from diagonals: the diagonals form a right triangle with each side. Side length s = √((d₁/2)² + (d₂/2)²). For d₁ = 12, d₂ = 6: s = √(36 + 9) = √45 ≈ 6.71. So our 12×6 tile has 6.71-inch sides.

Perimeter: P = 4 × s = 4 × √((d₁/2)² + (d₂/2)²).

Common error: treating a rhombus like a square because all sides are equal. A square is a special rhombus where the diagonals are also equal. Most rhombuses have different diagonals, so the shape is a stretched diamond rather than a square rotated 45°.