Rhombus Calculator
How It Works
A rhombus is a quadrilateral with four equal sides. Its diagonals bisect each other at right angles, which gives us the simple area formula: Area = (p x q) / 2, where p and q are the diagonal lengths. The side length can be found using the Pythagorean theorem on the half-diagonals.
Every square is a rhombus, but not every rhombus is a square. A rhombus becomes a square when both diagonals are equal. The opposite angles of a rhombus are equal, and adjacent angles are supplementary (add to 180 degrees).
Rhombuses appear in many contexts: diamond shapes in playing cards, tile patterns, crystal structures, and as the faces of some polyhedra like the rhombic dodecahedron. In engineering, rhombus-shaped linkages (like a pantograph) use the parallel properties of opposite sides.
Frequently Asked Questions
How do I find the area of a rhombus?
If you know the diagonals: Area = (d1 × d2) / 2. If you know the side and one angle: Area = s² × sin(angle). Both formulas give the same result.
What is the difference between a rhombus and a square?
A square is a special rhombus where all angles are 90° and both diagonals are equal. A general rhombus has two pairs of equal angles (acute and obtuse) and diagonals of different lengths.
Do the diagonals of a rhombus bisect each other?
Yes, the diagonals of a rhombus always bisect each other at right angles (90°). This is a key property that distinguishes rhombuses from general parallelograms, where diagonals bisect but not necessarily at right angles.
Is a diamond shape a rhombus?
In geometry, a "diamond" shape is indeed a rhombus oriented with one diagonal vertical. The diamond suits in playing cards are rhombus-shaped. In everyday language, "diamond" and "rhombus" are often used interchangeably.