How do you find the area of a rhombus from its diagonals?

Area = (p × q) ÷ 2, where p and q are the two diagonals. The diagonals of a rhombus always cross at right angles.

How do you find the side of a rhombus from its diagonals?

Each side = √((p/2)² + (q/2)²), because the half-diagonals form the legs of a right triangle whose hypotenuse is the side.

Does this tool upload anything?

No — all maths happens in your browser and no data is sent anywhere.

How is a rhombus different from a square?

Both have four equal sides, but a square also has four right angles. A rhombus can lean, so its angles are two pairs of equal (supplementary) angles. A square is a special rhombus where all angles are 90°.

Do the diagonals of a rhombus bisect each other?

Yes, and at right angles. The two diagonals cross at their midpoints and meet at 90°, which is why each side equals √((p/2)² + (q/2)²) from the half-diagonals.

How do I find the height from a side and angle?

The height equals side × sin θ, where θ is an interior angle. Since area also equals base × height, this gives the same area as side² × sin θ.

Rhombus Calculator — Gera Tools

A rhombus is a quadrilateral with four equal sides. This calculator solves it three ways — from both diagonals, from a side and height, or from a side and an interior angle — returning area, perimeter, side, height, the diagonals, and an angle.

How it works

The tool applies the standard rhombus relationships to whichever pair of values you provide:

From diagonals p and q: area = (p × q) ÷ 2 (the diagonals cross at right angles); side = √((p/2)² + (q/2)²); perimeter = 4 × side.
From side and height h: area = side × h.
From side and interior angle θ: area = side² × sin θ; height = side × sin θ; the diagonals follow from the law of cosines.

Perimeter is always 4 × side because all four sides are equal.

Example

A rhombus with diagonals p = 6 and q = 8:

Area = (6 × 8) ÷ 2 = 24
Side = √(3² + 4²) = √25 = 5
Perimeter = 4 × 5 = 20

Known	Area formula
Diagonals p, q	(p × q) ÷ 2
Side, height h	side × h
Side, angle θ	side² × sin θ

All calculations stay in your browser.