📏 Enter known values

Formula Reference

Worked example

Data

Side

\(b = {\color{#6c5ce7}{2\,\text{cm}}}\)

Area

\(a = \,?\)

Formula

\[a = \frac{3\cdot\sqrt{3}}{2}\cdot{{b}}^{2}\]

Steps

1Substitute the values

\[a = \frac{3\cdot\sqrt{3}}{2}\cdot{\left({\color{#6c5ce7}{2\,\text{cm}}}\right)}^{2}\]

Each letter is replaced by its value.

2Take the square root

\[a \approx \frac{3\cdot1.7321}{2}\cdot{\left({\color{#6c5ce7}{2\,\text{cm}}}\right)}^{2}\]

\(\sqrt{3} \approx 1.7321\)

3Square

\[a \approx \frac{3\cdot1.7321}{2}\cdot4\,\text{cm}^{2}\]

\(2 \times 2 = 4\)\(\text{cm} \times \text{cm} = \text{cm}^{2}\)

4Multiply

\[a \approx \frac{5.1962}{2}\cdot4\,\text{cm}^{2}\]

\(3\cdot1.7321 \approx 5.1962\)

5Divide

\[a \approx 2.5981\cdot4\,\text{cm}^{2}\]

\(\frac{5.1962}{2} \approx 2.5981\)

6Multiply

\[a \approx 2.5981\cdot4\,\text{cm}^{2} \approx 10.3923\,\text{cm}^{2}\]

\(2.5981\cdot4 \approx 10.3923\)

Area: 10.3923 cm²

Check

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

\[b = \sqrt{\frac{2\cdot{a}}{3\cdot\sqrt{3}}}\]

\[b = \sqrt{\frac{2\cdot10.3923\,\text{cm}^{2}}{3\cdot\sqrt{3}}} \approx 2\,\text{cm}\]

It gives 2 cm, the same as the value entered.

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Calculate the Area

Please fill in the fields:

Side

And leave empty

Area

Calculate the Side

Please fill in the fields:

Area

And leave empty

Side

How to calculate the area of a hexagon

A regular hexagon has six equal sides and six equal angles of 120°. It splits into six equilateral triangles whose side is the side of the hexagon, so its area is six times the area of one of those triangles:

\[ \text{Area} = \frac{3\sqrt{3}}{2} \times \text{Side}^2 \approx 2.598 \times \text{Side}^2 \]

If you know the area and need the side, solve for it:

\[ \text{Side} = \sqrt{\frac{2 \times \text{Area}}{3\sqrt{3}}} \]

These formulas are for regular hexagons. If the sides are different, split the shape into triangles or rectangles and add their areas.

How to use the calculator

Enter the side to get the area, or the area to get the side.
Leave the other field empty.
Press Calculate. The area comes out in the square of the side unit: a side in cm gives an area in cm².

Worked examples

1. Hexagon with a side of 4 cm

\[ \text{Area} = \frac{3\sqrt{3}}{2} \times 4^2 = 24\sqrt{3} \approx 41.57\ \text{cm}^2 \]

2. Side of a hexagon with an area of 100 m²

\[ \text{Side} = \sqrt{\frac{2 \times 100}{3\sqrt{3}}} \approx 6.2\ \text{m} \]

3. Hexagonal floor tiles

A tile has sides of 10 cm, so its area is \( 2.598 \times 10^2 \approx 259.8\ \text{cm}^2 \). One square meter is 10,000 cm², so you need about \( 10{,}000 \div 259.8 \approx 38.5 \) tiles per m². Round up and add a margin for the cuts at the edges.

Other measurements of a regular hexagon

Perimeter: \( P = 6 \times \text{Side} \).
Apothem (from the center to the middle of a side): \( a = \text{Side} \times \frac{\sqrt{3}}{2} \approx 0.866 \times \text{Side} \). The formula \( \text{Area} = \frac{P \times a}{2} \) gives the same result.
Across the corners: \( 2 \times \text{Side} \), the diameter of the circle that passes through the six corners.
Across the flats: \( \sqrt{3} \times \text{Side} \approx 1.732 \times \text{Side} \), the size you measure with a wrench on a hex nut.

Table of regular hexagons

Perimeter, apothem and area for sides from 1 to 10. The area is in the square of the side unit.

Side	Perimeter	Apothem	Area
1	6	0.87	2.6
2	12	1.73	10.39
3	18	2.6	23.38
4	24	3.46	41.57
5	30	4.33	64.95
6	36	5.2	93.53
7	42	6.06	127.31
8	48	6.93	166.28
9	54	7.79	210.44
10	60	8.66	259.81

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

🧱 Hexagonal Floor and Wall Tiles

Hexagon tiles are sold in boxes that cover a given surface. The area of one tile tells you how many pieces cover a floor, a backsplash or a shower wall, plus a margin for the cuts at the edges.

Avoids running short in the middle of the job or buying too many boxes

🌳 Gazebos, Decks and Garden Beds

Six-sided gazebos, raised beds and patios are common in garden design. The floor area sets how much decking, gravel, soil or sealant you need.

Turns a garden sketch into a material list

🐝 Beekeeping and Honeycombs

Bees build hexagonal cells because, among the shapes that tile a plane, the hexagon encloses the most area for a given perimeter. The area of one cell is used to estimate how much honey or brood a frame holds.

Connects geometry with an efficient design found in nature

🔩 Nuts, Bolts and Hex Bars

Hex nuts, bolt heads and hexagonal bar stock are measured across the flats. The cross-sectional area gives the weight of a bar per meter and is used in strength calculations.

Needed to estimate material weight and load capacity

📚 Homework and Exams

Regular polygons, the apothem and area problems are standard in school geometry. Many exercises give the side and ask for the area, or the other way around.

Lets students check a hand calculation step by step

🎲 Board Games and Maps

Many strategy games and simulation maps use a hexagonal grid. The area of one cell helps to scale a board to a table or to turn map cells into real surface.

Useful when designing or printing a custom board

Common Mistakes

⚠️ Using the Formula on an Irregular Hexagon

Common Error: The formula 3√3/2 × side² only works when all six sides and angles are equal. Applied to a hexagon with different sides, it gives a wrong area.

✅ Solution: Split an irregular hexagon into triangles or rectangles and add their areas

⚠️ Forgetting to Square the Side

Common Error: Multiplying 3√3/2 by the side instead of by the side squared. For a side of 4 this gives 10.39 instead of 41.57.

✅ Solution: Square the side first: 4² = 16, then multiply by 2.598

⚠️ Using the Apothem as the Side

Common Error: The apothem (from the center to the middle of a side) is shorter than the side. Using it as the side gives an area 25% too small.

✅ Solution: If you only know the apothem, the side is apothem × 2 ÷ √3

⚠️ Measuring Across the Flats

Common Error: On nuts and bars, the size you measure is the distance between opposite flat sides, not the side. That distance is √3 times the side.

✅ Solution: Divide the across-flats size by 1.732 to get the side

⚠️ Mixing Units

Common Error: Entering the side in centimeters and reading the area as if it were in square meters. 1 m² is 10,000 cm², not 100.

✅ Solution: Keep one unit and convert at the end: cm² ÷ 10,000 = m²

⚠️ Rounding √3 Too Early

Common Error: Using 1.7 for √3 makes every result about 2% low, which matters when ordering material for large surfaces.

✅ Solution: Use √3 ≈ 1.732 or let the calculator keep full precision

Applications by Industry

Construction & Architecture

Paving: Number of hexagonal pavers or concrete tiles for patios and sidewalks
Facades: Surface of hexagonal panels and cladding modules
Pavilions: Floor slab of hexagonal gazebos, kiosks and towers

Manufacturing

Bar stock: Cross-sectional area of hexagonal steel and brass bars to get the weight per meter
Fasteners: Bearing surface of hex nuts and bolt heads
Packaging: Area of hexagonal boxes and lids to estimate cardboard per unit

Chemistry & Materials

Graphene: Area of the hexagonal cell to relate the number of atoms to the surface
Crystals: Faces of hexagonal crystals such as quartz and snowflakes
Honeycomb panels: Cell size in lightweight panels used in aircraft and doors

Agriculture & Beekeeping

Hives: Area of honeycomb cells per frame to estimate production
Planting: Hexagonal planting layouts, which fit about 15% more plants than a square grid with the same spacing
Irrigation: Coverage of sprinklers arranged in a hexagonal pattern