📏 Enter known values

Formula Reference

Worked example

Data

Diagonal 1

\(b = {\color{#6c5ce7}{6\,\text{cm}}}\)

Diagonal 2

\(c = {\color{#6c5ce7}{4\,\text{cm}}}\)

Area

\(a = \,?\)

Formula

\[a = \frac{{b}\cdot{c}}{2}\]

Steps

1Substitute the values

\[a = \frac{{\color{#6c5ce7}{6\,\text{cm}}}\cdot{\color{#6c5ce7}{4\,\text{cm}}}}{2}\]

Each letter is replaced by its value.

2Multiply

\[a = \frac{24\,\text{cm}^{2}}{2}\]

\(6\cdot4 = 24\)\(\text{cm} \times \text{cm} = \text{cm}^{2}\)

3Divide

\[a = \frac{24\,\text{cm}^{2}}{2} = 12\,\text{cm}^{2}\]

\(\frac{24}{2} = 12\)

Area: 12 cm²

Check

If we use the result to calculate Diagonal 1, we should get the value you entered:

\[b = \frac{2\cdot{a}}{{c}}\]

\[b = \frac{2\cdot12\,\text{cm}^{2}}{4\,\text{cm}} = 6\,\text{cm}\]

It gives 6 cm, the same as the value entered.

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Calculate the Area

Please fill in the fields:

Diagonal_1 Diagonal_2

And leave empty

Area

Calculate the Diagonal_1

Please fill in the fields:

Area Diagonal_2

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Diagonal_1

Calculate the Diagonal_2

Please fill in the fields:

Area Diagonal_1

And leave empty

Diagonal_2

How to calculate the area of a rhombus

A rhombus has four equal sides, and its diagonals cross at right angles at their midpoints. The diagonals split it into four equal right triangles, so its area is half the product of the diagonals:

\[ \text{Area} = \frac{\text{Diagonal}_1 \times \text{Diagonal}_2}{2} \]

If you know the area and one diagonal, the other one is:

\[ \text{Diagonal}_2 = \frac{2 \times \text{Area}}{\text{Diagonal}_1} \]

How to use the calculator

Enter two of the three values: the area and the two diagonals.
Leave empty the one you want to find.
Press Calculate. Both diagonals must be in the same unit.

Worked examples

1. Diagonals of 10 cm and 6 cm

\[ \text{Area} = \frac{10 \times 6}{2} = 30\ \text{cm}^2 \]

2. Second diagonal of a rhombus with an area of 48 m² and a diagonal of 12 m

\[ \text{Diagonal}_2 = \frac{2 \times 48}{12} = 8\ \text{m} \]

3. Fabric for a diamond kite

The frame sticks of a diamond kite are its diagonals: 80 cm and 50 cm. The sail needs \( 80 \times 50 \div 2 = 2{,}000\ \text{cm}^2 \), that is, 0.2 m², plus a margin for the hems.

Side of a rhombus from its diagonals

Each side is the hypotenuse of a right triangle whose legs are half of each diagonal:

\[ \text{Side} = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2} \]

With diagonals of 10 and 6, the side is \( \sqrt{5^2 + 3^2} = \sqrt{34} \approx 5.83 \) and the perimeter is \( 4 \times 5.83 \approx 23.32 \).

Other ways to find the area

With the side \( s \) and the height \( h \): \( A = s \times h \), as in any parallelogram.
With the side and an angle \( \alpha \): \( A = s^2 \times \sin \alpha \).
A square is a rhombus with equal diagonals: \( A = d^2 \div 2 \).

Diagonals, area and side of common rhombuses

Diagonal 1	Diagonal 2	Area	Side
6	4	12	3.61
8	6	24	5
10	6	30	5.83
10	8	40	6.4
12	5	30	6.5
16	12	96	10
24	10	120	13
30	16	240	17

When Do You Need to Calculate the Area of a Rhombus?

🪁 Kites and Banners

Diamond kites and many flags and banners are rhombuses. The diagonals are easy to measure (on a kite they are the frame sticks), so the fabric area comes straight from them.

Gives the fabric needed from the length of the frame

🧱 Diamond Tiles and Flooring

Diamond tiles, parquet pieces and wall panels are sold by surface. With the diagonals of one piece you know how many cover a room.

Helps estimate the pieces and boxes to buy

💎 Jewelry and Inlays

Diamond-shaped pendants, inlays and some gem facets are rhombuses. Their area is used to estimate sheet metal or the size of a setting.

Useful for material and cost estimates in small parts

🚸 Road Signs and Markings

Diamond warning signs and some road markings are rhombuses, often squares turned 45°. Their area sets the reflective sheeting and the paint needed.

Sizes signs and painted symbols

📐 Geometry Problems

Exercises on rhombuses usually give the diagonals, or one diagonal and the side. Knowing that the diagonals are perpendicular is the key to solving them.

Practice with right triangles inside a quadrilateral

🪟 Lattices and Leaded Windows

Lattice fences, leaded windows and trellises are made of many rhombuses. The area of one cell tells you how much glass, mesh or open space there is.

Plans glass pieces and the open area of a trellis

Common Mistakes

⚠️ Forgetting to Divide by 2

Common Error: Multiplying the diagonals and stopping there. That is the area of the rectangle around the rhombus, twice the real area.

✅ Solution: Area = d₁ × d₂ ÷ 2

⚠️ Using the Side as a Diagonal

Common Error: The side is the edge of the rhombus; the diagonals join opposite corners. Mixing them up gives a wrong area.

✅ Solution: The diagonals cross in the middle: measure from one corner to the opposite one

⚠️ Squaring the Side

Common Error: Writing side² as for a square. A rhombus with the same side has a smaller area unless its angles are 90°.

✅ Solution: Use side² × sin(angle), or the diagonals

⚠️ Using Half-Diagonals

Common Error: Measuring from the center to a corner gives half a diagonal. Using those halves in the formula gives an area four times smaller.

✅ Solution: Double the half-diagonals before using the formula

⚠️ Assuming Equal Diagonals

Common Error: Only a square has equal diagonals. Assuming d₁ = d₂ for any rhombus overestimates the area.

✅ Solution: Measure both diagonals

⚠️ Mixing Units

Common Error: Entering one diagonal in centimeters and the other in meters.

✅ Solution: Convert both diagonals to the same unit first

Applications by Industry

Construction & Interior Design

Flooring: Diamond tiles and parquet patterns
Facades: Rhombus-shaped cladding panels and screens
Lattices: Wooden and metal trellises with diamond openings

Transportation & Signage

Warning signs: Reflective sheeting for diamond signs
Markings: Paint for diamond symbols on roads and lanes
Wayfinding: Rhombus panels in signage systems

Jewelry & Crafts

Pendants: Metal sheet for diamond-shaped pieces
Mosaics: Rhombus tiles in glass and ceramic mosaics
Quilting: Diamond blocks in star quilt patterns

Kites & Sports

Kites: Sail area from the frame sticks
Baseball: The infield, a square turned into a diamond
Flags: Rhombus shapes in flag and banner designs

Science

Crystals: Rhombic faces in crystal structures
Optics: Rhomboid prisms that shift light beams sideways
Lattices: 2D lattice cells shaped as rhombuses, as in graphene

Education

Geometry: Area with diagonals as an application of perpendicular lines
Proofs: Showing that the diagonals bisect each other at 90°
Exams: Problems that combine the Pythagorean theorem and the area of a rhombus