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Generated on: July 20, 2026 at 09:33 PM

Rhombus Area Calculator

Inputs

Known valuesDiagonals
Diagonal 16
Diagonal 28
Base5
Height (perpendicular)4
Side length5
Interior angle60 °

Visualization

Rhombus with diagonals p and qA rhombus drawn with its two diagonals p and q crossing at right angles in the centre, splitting the figure into four congruent right triangles. p q
Rhombus with base b and height hA rhombus resting on base b, with the perpendicular height h shown as a dashed construction line to the opposite side. b h
Rhombus with side a and interior angle θA rhombus with equal side a and an interior angle θ marked at one vertex between two adjacent sides. a θ

Generated with OneCalc · https://onecalc.app/en/math/rhombus-area

Mathematics

Rhombus Area Calculator

Find the area and perimeter of a rhombus from its diagonals, base and height, or side and angle. Applies A = pq/2, A = b × h, or A = a² sin θ with full step-by-step working.

Inputs

Rhombus with diagonals p and qA rhombus drawn with its two diagonals p and q crossing at right angles in the centre, splitting the figure into four congruent right triangles. p q

Results

Enter a value to see results.

\begin{aligned} A &= \dfrac{p \, q}{2} \\ &= \dfrac{(6)(8)}{2} \\ &= ? \end{aligned}
\begin{aligned} s &= \sqrt{\left(\tfrac{p}{2}\right)^2 + \left(\tfrac{q}{2}\right)^2} \\ &= \sqrt{\left(\tfrac{6}{2}\right)^2 + \left(\tfrac{8}{2}\right)^2} \\ &= ? \end{aligned}
\begin{aligned} P &= 4s \\ &= 4 \times ? \\ &= ? \end{aligned}

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What a rhombus is

A rhombus is a quadrilateral with four equal sides. It is a special parallelogram, so opposite sides are parallel and opposite angles are equal. Its diagonals are perpendicular to each other and bisect each other, which gives the rhombus several handy ways to compute its area. This calculator covers three of them — the diagonals, the base and perpendicular height, and one side together with an interior angle — and always returns the perimeter as well.

Area from the diagonals

The most common method uses the two diagonals pp and qq:

A=p q2A = \frac{p \, q}{2}

The diagonals cross at right angles and cut each other in half, so they divide the rhombus into four congruent right triangles. Adding their areas reproduces the formula above.

Worked example

A rhombus has diagonals of 6 cm and 8 cm.

A=6×82=24 cm2A = \frac{6 \times 8}{2} = 24 \text{ cm}^2

To find the side, each half-diagonal forms the legs of a right triangle:

a=(62)2+(82)2=9+16=5 cma = \sqrt{\left(\tfrac{6}{2}\right)^2 + \left(\tfrac{8}{2}\right)^2} = \sqrt{9 + 16} = 5 \text{ cm}

so the perimeter is P=4×5=20P = 4 \times 5 = 20 cm.

Area from base and height

Because a rhombus is a parallelogram, its area is the base times the perpendicular height:

A=b×hA = b \times h

Here hh is the perpendicular distance between two opposite sides, not the slant length. With a base of 5 cm and a height of 4 cm, A=5×4=20A = 5 \times 4 = 20 cm².

Area from a side and an angle

When one side aa and an interior angle θ\theta are known, the area is:

A=a2sin⁡θA = a^2 \sin\theta

This follows from the parallelogram area A=a×(asin⁡θ)A = a \times (a\sin\theta), where asin⁡θa\sin\theta is the height. For a=5a = 5 cm and θ=60°\theta = 60°:

A=25×sin⁡60°≈21.65 cm2A = 25 \times \sin 60° \approx 21.65 \text{ cm}^2

Either interior angle works, because an angle and its supplement share the same sine.

ShapeArea formula
SquareA=a2A = a^2 (rhombus with right angles)
ParallelogramA=b×hA = b \times h (rhombus drops the equal-sides rule)
KiteA=12pqA = \tfrac{1}{2} p q (diagonals perpendicular, as here)

Frequently Asked Questions (FAQ)

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

Multiply the two diagonals and divide by two: A = (p × q) ÷ 2. The diagonals of a rhombus cross at right angles and bisect each other, so this is exact. For example, diagonals of 6 cm and 8 cm give A = (6 × 8) ÷ 2 = 24 cm².

What is the perimeter of a rhombus?

Because all four sides of a rhombus are equal, the perimeter is simply four times the side length: P = 4a. If you only know the diagonals, first find the side with a = √((p÷2)² + (q÷2)²), then multiply by four.

Is a rhombus a parallelogram?

Yes. A rhombus is a parallelogram in which all four sides are equal in length. That means the parallelogram area formula A = base × perpendicular height applies to a rhombus as well, alongside the diagonal formula.

How do you find the area from a side and an angle?

When you know one side a and an interior angle θ, the area is A = a² × sin(θ). The result is the same for either interior angle, since an angle and its supplement have the same sine. For a = 5 cm and θ = 60°: A = 25 × sin(60°) ≈ 21.65 cm².

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