Rhombus Calculator

Calculate all properties of a rhombus including area, perimeter, diagonals, side length, and angles. Supports multiple input methods for maximum flexibility.

Length of first diagonal (required if using diagonals)

Length of second diagonal (required if using diagonals)

Length of one side (required for side-based methods)

Interior angle in degrees (required if using angle method)

Perpendicular height (required if using height method)

Area = (d₁ * d₂) / 2 Area = side^2 * sin(θ) Area = side * height Perimeter = 4 * side Side = sqrt((d₁/2)^2 + (d₂/2)^2) Height = side * sin(θ) d₁^2 + d₂^2 = 4 * side^2 Where: d₁, d₂ = diagonals (bisect at 90deg) side = length of any side θ = interior angle height = perpendicular distance
Example 1 (From Diagonals): Diagonal 1 = 10 cm Diagonal 2 = 8 cm Area = (10 * 8) / 2 = 40 cm^2 Side = sqrt(5^2 + 4^2) = 6.40 cm Perimeter = 4 * 6.40 = 25.61 cm Height = 40 / 6.40 = 6.25 cm Example 2 (From Side & Angle): Side = 7 in Angle = 60deg Area = 7^2 * sin(60deg) = 42.44 in^2 Perimeter = 4 * 7 = 28 in Height = 7 * sin(60deg) = 6.06 in Diagonal 1 = 7sqrt(2+sqrt3) ≈ 12.12 in Diagonal 2 = 7sqrt(2-sqrt3) ≈ 7.00 in Example 3 (From Side & Height): Side = 8 m Height = 6 m Area = 8 * 6 = 48 m^2 Perimeter = 4 * 8 = 32 m Angle = arcsin(6/8) = 48.59deg

What is a rhombus?

A rhombus is a quadrilateral with all four sides equal in length. It is a special type of parallelogram where opposite sides are parallel and opposite angles are equal. A square is a special rhombus with all angles equal to 90deg.

What is the formula for the area of a rhombus?

There are three common formulas for rhombus area: (1) Area = (d₁ * d₂)/2 using diagonals, (2) Area = side * height using base and height, (3) Area = side^2 * sin(θ) using side and angle. For diagonals 10 cm and 8 cm: Area = (10 * 8)/2 = 40 cm^2.

How do I calculate the perimeter of a rhombus?

Since all sides are equal, the perimeter is: Perimeter = 4 * side. For a rhombus with side length 7 cm: Perimeter = 4 * 7 = 28 cm. This is simpler than other quadrilaterals because you only need one side measurement.

What are the diagonals of a rhombus?

The diagonals of a rhombus bisect each other at right angles (90deg). They are generally not equal in length, except in a square. The diagonals divide the rhombus into 4 right triangles. If you know both diagonals, you can find the side: side = sqrt((d₁/2)^2 + (d₂/2)^2).

How do I find the height of a rhombus?

The height is the perpendicular distance between opposite sides. It can be calculated from the side and angle: height = side * sin(θ), where θ is any interior angle. You can also use: height = (d₁ * d₂)/(2 * side) from the diagonals.

What are the angle properties of a rhombus?

In a rhombus: opposite angles are equal, adjacent angles are supplementary (sum to 180deg), all four angles sum to 360deg, and the diagonals bisect the angles. If one angle is 60deg, the opposite is also 60deg, and the other two are each 120deg.

What is the relationship between the diagonals and sides?

The diagonals and side length are related by the Pythagorean theorem: side^2 = (d₁/2)^2 + (d₂/2)^2, since the diagonals bisect each other at right angles. This means: side = sqrt((d₁^2 + d₂^2)/4).

What is the difference between a rhombus and a square?

A square is a special rhombus where all angles are 90deg and both diagonals are equal. All squares are rhombuses, but not all rhombuses are squares. In a rhombus, angles can be any value (as long as adjacent angles are supplementary).

What are real-world applications of rhombus calculations?

Rhombuses appear in: diamond and kite shapes, decorative tile patterns, playing card suit symbols (diamonds), crystal structures, lattice frameworks, road signs (like yield signs in some countries), architectural designs, and textile patterns.

Can I calculate a rhombus from just the area and one diagonal?

Yes! If you know the area and one diagonal (d₁), you can find the other diagonal: d₂ = (2 * Area)/d₁. Then you can calculate the side length and all other properties using the formulas.