Rhombus Calculator
Calculate the area, perimeter, diagonals, side length, and interior angles of a rhombus. Choose from three input methods depending on what measurements you have.
A rhombus is a quadrilateral with all four sides equal in length. It is a special case of a parallelogram where all sides are the same, and its diagonals bisect each other at right angles.
Key Formulas:
Area (from diagonals): Area = (d1 x d2) / 2
Area (from side and angle): Area = a² x sin(α)
Perimeter: P = 4a (since all sides are equal)
Side from diagonals: a = sqrt((d1/2)² + (d2/2)²)
Diagonals from side and angle: d1 = 2a x sin(α/2), d2 = 2a x cos(α/2)
Properties of a Rhombus:
- All four sides are equal in length
- Opposite angles are equal
- Adjacent angles are supplementary (add up to 180°)
- Diagonals bisect each other at right angles (90°)
- Diagonals bisect the vertex angles
- A square is a special rhombus where all angles are 90°
Example:
A rhombus with diagonals d1 = 10 and d2 = 8:
- Area = (10 x 8) / 2 = 40
- Side = sqrt(5² + 4²) = sqrt(41) = 6.403
- Perimeter = 4 x 6.403 = 25.612