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Rhombus Area Calculator

Geometry

Calculation mode

Diagonal 1 (d₁)

Diagonal 2 (d₂)

Length unit

Output area unit

Decimal precision

d₁ = 10 md₂ = 6 m
Area = 30 m²
Perimeter = 23.3238 m

Derived side: 5.831 m

A = (d₁ × d₂) / 2 = (10 × 6) / 2

Step-by-step

1. Formula: A = (d₁ × d₂) / 2

2. Substitute: A = (10 × 6) / 2

3. Convert to meters: d₁ = 10.000000 m, d₂ = 6.000000 m

4. Compute: A = (10.000000 × 6.000000) / 2 = 30.000000 m²

5. Derived side: a = √((d₁/2)² + (d₂/2)²) = √((10/2)² + (6/2)²) = 5.830952 m

6. Convert to m²: 30.000000 m² × 1 = 30 m²

7. Perimeter: P = 4 × a = 4 × 5.830952 = 23.3238 m

Area in other units

mm²3,00,00,000
cm²3,00,000
m²30
km²0
in²46,500.093
ft²322.917
yd²35.88

About This Tool

Rhombus Area Calculator – Three Methods, Instant Results

A rhombus is a quadrilateral in which all four sides are equal in length. It resembles a diamond or tilted square and appears in architecture, engineering, tile design, gemology, and coordinate geometry. This calculator computes the area and perimeter of any rhombus using three flexible methods — diagonals, base and height, or side and angle — so you can solve whatever measurements you have on hand.

Method 1 — Diagonals

The most common textbook formula uses the two diagonals of a rhombus:

A = (d₁ × d₂) / 2

where d₁ and d₂ are the lengths of the two diagonals. Because the diagonals of a rhombus always bisect each other at right angles, this formula is exact for every rhombus regardless of angle. The calculator also derives the side length in this mode using the Pythagorean theorem applied to the four right triangles formed by the half-diagonals:

a = √((d₁/2)² + (d₂/2)²)

Example: a rhombus with diagonals of 10 cm and 6 cm has an area of (10 × 6) / 2 = 30 cm² and a derived side of approximately 5.83 cm.

Method 2 — Base and Height

When you know any side length and the perpendicular height, use:

A = a × h

Here a is the side length (which equals the base, since all sides are equal) and h is the perpendicular distance between the two parallel sides — not the slant height. This is the most intuitive formula and is equivalent to treating the rhombus as a parallelogram, since a rhombus is a special case of a parallelogram.

Example: a rhombus with side = 8 m and perpendicular height = 5 m has an area of 8 × 5 = 40 m².

Method 3 — Side and Angle

When you know the side length and one interior angle, the trigonometric formula applies:

A = a² × sin(θ)

where a is the side length and θ is one of the interior angles. Because opposite angles in a rhombus are equal and adjacent angles are supplementary, you only need one angle value. The calculator accepts the angle in either degrees or radians.

Example: a rhombus with side = 7 cm and interior angle = 60° has an area of 7² × sin(60°) = 49 × 0.866 ≈ 42.44 cm².

Perimeter of a Rhombus

Since all four sides of a rhombus are equal, the perimeter is simply:

P = 4 × a

This calculator displays the perimeter alongside the area in every mode. In Diagonals mode, the side length is derived first, and the perimeter follows from it.

Unit Support and Precision

Input measurements can be entered in any standard length unit — mm, cm, m, km, in, ft, yd, or mi. All values are converted to meters internally before computation. The area result is then converted to your chosen output unit (mm², cm², m², km², in², ft², or yd²), and the conversion table shows the area in every unit simultaneously. Decimal precision is configurable from 0 to 10 places.

Common Applications

Rhombus-shaped areas appear in many real-world contexts:

  • Tile and flooring design — diamond-pattern tiles are rhombuses; calculating material requirements needs accurate area figures.
  • Gemology — gemstone facets (particularly in brilliant cuts) often approximate rhombus shapes.
  • Structural engineering — diagonal bracing creates rhombus-shaped panels whose area determines load distribution.
  • Surveying and land measurement — plots bounded by equal-length fences or walls can be rhombus-shaped.
  • Coordinate geometry — computing rhombus area from vertex coordinates is a standard problem in analytic geometry and competitive mathematics.

Rhombus vs. Square vs. Parallelogram

A square is a rhombus with all interior angles equal to 90°. When θ = 90°, the formula a² × sin(90°) = a² correctly reduces to the square area formula. A rhombus is also a special parallelogram — one with all equal sides — so all parallelogram area formulas apply to rhombuses as well. The diagonal formula, however, works only for rhombuses (not general parallelograms) because the diagonals must be perpendicular bisectors of each other.

How the Calculator Works

Select the calculation mode matching the measurements you have. Enter the required values, choose your preferred length and output area units, set the precision, and the area and perimeter appear instantly. A step-by-step breakdown shows each arithmetic step, and an area conversion table lists the result in all supported units. Use the Copy button to transfer the area value to your clipboard, or Reset to start fresh with the default values.

Frequently Asked Questions

Is the Rhombus Area Calculator free?

Yes, Rhombus Area Calculator is totally free :)

Can I use the Rhombus Area Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Rhombus Area Calculator?

Yes, any data related to Rhombus Area Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

What are the three ways to calculate the area of a rhombus?

A rhombus area can be computed using three methods: (1) Diagonals — Area = (d₁ × d₂) / 2, where d₁ and d₂ are the two diagonals; (2) Base and Height — Area = a × h, where a is any side and h is the perpendicular height; (3) Side and Angle — Area = a² × sin(θ), where a is the side length and θ is one interior angle.

How does this calculator work?

Select a calculation mode — Diagonals, Base & Height, or Side & Angle — then enter the required measurements. The tool instantly computes the area in your chosen output unit, along with the perimeter and (in Diagonals mode) the derived side length. A step-by-step breakdown and an area conversion table are also shown.

What is a rhombus and how is it different from a square?

A rhombus is a quadrilateral with four equal-length sides. Its angles are not necessarily 90°, so it looks like a 'tilted' square. A square is actually a special rhombus where all four interior angles are exactly 90°. The diagonal and side-angle formulas work for both; the base-height formula gives the same result as side² when θ = 90°.

Why do the diagonals of a rhombus bisect each other at right angles?

Because opposite sides of a rhombus are parallel and all sides are equal, the diagonals always intersect at 90° and bisect each other. This property is what makes the diagonal formula Area = (d₁ × d₂) / 2 exact — it is equivalent to calculating two right triangles formed by the half-diagonals.

Can I use different units for input and output?

Yes. Choose any length unit (mm, cm, m, km, in, ft, yd, mi) for your input measurements, and independently choose any area unit (mm², cm², m², km², in², ft², yd²) for the output. The calculator converts all lengths to meters internally, computes the area in m², then converts to the selected output unit.

How accurate are the results?

Results use standard IEEE 754 double-precision floating-point arithmetic (JavaScript Number). You can set precision from 0 to 10 decimal places. Accuracy depends on the precision of your inputs; the calculator does not introduce additional rounding errors beyond what JavaScript's Math.sin() and standard arithmetic provide.