Calculator Input
Choose one known measurement, enter its value, and the calculator converts it into complete regular hexagon properties.
Plotly Graph
The chart below draws the regular hexagon using the calculated circumradius, which equals the side length.
Example Data Table
| Side Length | Perimeter | Area | Apothem | Long Diagonal | Short Diagonal |
|---|---|---|---|---|---|
| 4 cm | 24 cm | 41.57 cm² | 3.46 cm | 8 cm | 6.93 cm |
| 6 cm | 36 cm | 93.53 cm² | 5.20 cm | 12 cm | 10.39 cm |
| 8 cm | 48 cm | 166.28 cm² | 6.93 cm | 16 cm | 13.86 cm |
| 10 cm | 60 cm | 259.81 cm² | 8.66 cm | 20 cm | 17.32 cm |
Formula Used
Let side length = s
- Perimeter = 6s
- Area = (3√3 / 2) × s²
- Apothem = (√3 / 2) × s
- Circumradius = s
- Inradius = Apothem
- Long Diagonal = 2s
- Short Diagonal = √3 × s
- Flat-to-Flat Distance = √3 × s
- Point-to-Point Distance = 2s
- Interior Angle = 120°
- Exterior Angle = 60°
- Central Angle = 60°
Reverse formulas for side length
- From perimeter: s = P / 6
- From area: s = √(2A / 3√3)
- From apothem: s = 2a / √3
- From circumradius: s = R
- From long diagonal: s = Dₗ / 2
- From short diagonal: s = Dₛ / √3
How to Use This Calculator
- Select the known hexagon measurement from the dropdown.
- Enter the numeric value for that measurement.
- Add a unit label such as cm, m, ft, or in.
- Choose how many decimal places you want displayed.
- Press Calculate Hexagon to generate the full result set.
- Review the values shown above the form and use the export buttons if needed.
Frequently Asked Questions
1) What makes a regular hexagon special?
A regular hexagon has six equal sides and six equal angles. Its symmetry makes formulas simple, especially because the circumradius always equals the side length.
2) Can I calculate everything from only one value?
Yes. For a regular hexagon, one reliable measurement such as side, area, perimeter, apothem, or a diagonal is enough to derive the other main properties.
3) Why does the side length equal the circumradius?
A regular hexagon fits exactly inside a circle using six central angles of 60 degrees. That creates six equilateral triangles, making the circle radius equal to each side.
4) What is the difference between the long and short diagonal?
The long diagonal connects opposite vertices and equals twice the side length. The short diagonal skips one vertex and equals the side length multiplied by square root of three.
5) Is apothem the same as inradius?
Yes. In a regular hexagon, the apothem is the distance from the center to any side, which is also the inradius of the inscribed circle.
6) Which units should I use?
Use any consistent unit you like, including millimeters, centimeters, meters, inches, or feet. Area values will automatically correspond to squared versions of your chosen unit.
7) Does rounding affect engineering or design work?
It can. Use more decimal places when precision matters for fabrication, CAD, or layout planning. For classroom work, fewer decimals are usually enough for neat presentation.
8) What happens if I enter area instead of side?
The calculator first converts the area into side length using the reverse area formula. Then it computes perimeter, apothem, diagonals, angles, and other related dimensions.