Rhombus Calculator

A rhombus is defined entirely by two independent measurements: its side length a and one interior angle θ. Because all four sides are equal, the perimeter is simply P = 4a. Opposite angles of a rhombus are equal, and adjacent angles are supplementary, meaning if one acute angle is θ, the obtuse angle is 180° − θ. The height — the perpendicular distance between two parallel sides — is h = a sin(θ), which is also the basis for the area formula A = a² sin(θ).

The two diagonals of a rhombus bisect each other at right angles. Using trigonometry on the half-triangles formed at the centre, the shorter diagonal is d₁ = 2a sin(θ/2) and the longer diagonal is d₂ = 2a cos(θ/2). An equivalent area formula is A = (d₁ × d₂) / 2, which is particularly useful when the diagonals are known directly rather than the angle. Both formulas are mathematically identical and produce the same result.

Practical applications of rhombus geometry appear across many fields. In structural engineering, diagonal bracing members often form rhombus or diamond patterns to distribute lateral loads. In crystallography, the unit cells of certain crystal lattices are rhombic. In textile and tile design, repeating diamond patterns are constructed from rhombuses with specific aspect ratios. Surveyors and GIS professionals use parallelogram and rhombus properties when computing areas of land parcels with equal-length boundaries.

This calculator requires the acute interior angle θ to be strictly between 0° and 90° exclusive. At θ = 90°, the rhombus becomes a square, which is a valid special case: enter 90° to obtain the square's properties. Angles of 0° or 180° produce degenerate flat shapes with zero area and are mathematically undefined in this context. If you know the two diagonals but not the angle, you can derive the angle from θ = 2 arcsin(d₁ / (2a)) before using this calculator. All calculations assume a flat (Euclidean) plane; rhombus geometry on curved surfaces such as spheres or hyperbolic planes requires non-Euclidean formulas. Floating-point precision limits apply for very small angles near 0° or very large side values.