Calculator
Formula Used
The main side based formula is:
Area = (3 × √3 ÷ 2) × s²
Here, s is the side length of the regular hexagon.
Other useful formulas
- Perimeter = 6s
- Apothem = (√3 ÷ 2) × s
- Circumradius = s
- Across flats = √3 × s
- Across corners = 2s
- Area from apothem = 2√3 × a²
- Area from perimeter = (√3 ÷ 24) × P²
How to Use This Calculator
- Enter a project name if you want a labeled report.
- Select the known measurement type.
- Enter the measurement value as a positive number.
- Choose the unit used in your drawing or problem.
- Select the number of decimal places.
- Press the calculate button.
- Review the area and related hexagon measurements.
- Use the CSV or PDF button for saving results.
Example Data Table
| Known Input | Value | Side Length | Area Formula | Approx Area |
|---|---|---|---|---|
| Side length | 10 cm | 10 cm | (3√3 / 2) × 10² | 259.8076 cm² |
| Apothem | 8 cm | 9.2376 cm | 2√3 × 8² | 221.7025 cm² |
| Perimeter | 72 cm | 12 cm | (3√3 / 2) × 12² | 374.1229 cm² |
| Across corners | 20 cm | 10 cm | (3√3 / 2) × 10² | 259.8076 cm² |
Regular Hexagon Area Guide
Overview
A regular hexagon is a six sided polygon with equal sides. It also has equal interior angles. This makes its area simple to calculate when one reliable measure is known. The most common input is side length. Many plans, tile layouts, honeycomb patterns, nuts, bolts, and classroom problems use that value.
Why This Shape Matters
A regular hexagon fits tightly with other identical hexagons. There are no gaps between neighbors. This property makes it useful in flooring, paving, packaging, machining, and graphic design. The shape also divides into six equal equilateral triangles. Each triangle has the same side as the hexagon. The total area is therefore six times one triangle area.
Main Measurements
The side is the length of one outer edge. The apothem is the distance from the center to any side. The circumradius is the distance from the center to any corner. In a regular hexagon, the circumradius equals the side. The inradius equals the apothem. Across flats measures the distance between two opposite sides. Across corners measures the distance between two opposite vertices.
Using Different Inputs
This calculator accepts side, apothem, circumradius, inradius, perimeter, across flats, and across corners. It converts the chosen input into side length first. Then it calculates area and all related measures. This method keeps the output consistent. It also helps compare drawings that use different labels.
Accuracy Tips
Use the same unit for the input value. Choose decimal places based on your project. For construction estimates, rounding may be enough. For technical drawings, use more decimals. Always check that the value is positive. A zero or negative measure cannot form a real regular hexagon.
Practical Uses
Students can verify homework steps. Designers can estimate repeated tile coverage. Builders can compare pattern layouts. Machinists can check flats and corners on hex parts. The downloadable CSV helps with records. The PDF option gives a neat report for printing or sharing.
Final Note
A regular hexagon is simple, but its linked measurements are powerful. One input can reveal the full geometry. This makes planning faster and easier. It also reduces repeated manual work. Clear outputs let users spot mistakes before materials are ordered. That can save cost, time, and confusion during daily planning.
FAQs
What is a regular hexagon?
A regular hexagon has six equal sides and six equal angles. Each interior angle is 120 degrees. Because all sides match, one side length can calculate area, perimeter, radius, and diagonals.
What is the area formula for a regular hexagon?
The standard formula is Area = (3√3 / 2) × s². The letter s means side length. This formula comes from splitting the hexagon into six equal equilateral triangles.
Can I calculate area from apothem?
Yes. If the apothem is known, the calculator converts it to side length. You can also use Area = 2√3 × a², where a is the apothem.
Is circumradius equal to side length?
Yes. In a regular hexagon, the distance from center to any corner equals the side length. This makes circumradius based calculations direct and simple.
What does across flats mean?
Across flats is the distance between two opposite parallel sides. It equals two times the apothem. It is also the short diagonal of a regular hexagon.
What does across corners mean?
Across corners is the distance between two opposite vertices. It equals the long diagonal. For a regular hexagon, it is two times the side length.
Can this calculator help with tiles?
Yes. It can estimate the area of one regular hexagon tile. You can multiply the result by the number of tiles to estimate total coverage.
Why are my results rounded?
Results use the decimal places you select. Increase the decimal setting for more precision. Use fewer decimals when you only need a simple estimate.