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Properties of a Rhombus

This tool calculates the basic geometric properties of a rhombus (also called diamond shape). Enter below the shape dimensions. The calculated results will have the same units as your input. Please use consistent units for any input.

Known data:
Sides and angle Diagonals
α =
φ1 =		deg rad
p =
q =
Geometric properties:
Area =
Perimeter =
Lengths:
Side α =
Diagonal p =
Diagonal q =
Height h =
Angles :	deg rad
φ1 =
φ2 =
Inscribed circle:
Radius r =

Definitions

Geometry

Rhombus (also called diamond shape) is a quadrilateral shape with all four sides equal. Pairs of opposite sides are parallel and pairs of opposite angles are equal. Therefore rhombus is also a parallelogram and features all parallelogram properties. It differs from square in its interior angles which are not all equal and 90°.

The area of a rhombus is given by the formulas:

where a the length of the sides and h the height, perpendicular to a side from an opposite vertex. Height h can be found, using any of the right triangles, with hypotenuse α shown in figure below:

Interior angle φ₂is supplementary with φ₁. Therefore:

Diagonals p and q of rhombus are mutually bisecting each other, and they also bisect the interior angles φ₁and φ₂. Diagonals can be expressed in terms of side lengths and interior angles as:

The perimeter of a parallelogram is simply the sum of the lengths of all sides:

The radius of the inscribed circle, can be determined, using the right triangle, with hypotenuse (see figure below):