Regular Hexagon Calculator
Enter one known value for a regular hexagon (all six sides equal), and this tool calculates the rest instantly.
- Perimeter: P = 6s
- Area: A = (3√3/2)s²
- Apothem: a = (√3/2)s
What is a Hexagon?
A hexagon is a six-sided polygon. In this calculator and article, we focus on the regular hexagon, which has equal side lengths and equal interior angles. Regular hexagons appear everywhere: honeycombs, bolt heads, floor tiles, game maps, mesh structures, and architecture.
The regular hexagon is especially practical because it breaks cleanly into six equilateral triangles. That relationship makes calculations easier and gives the shape excellent symmetry.
How to Use This Hexagon Calculator
- Select the measurement you already know (side, area, perimeter, etc.).
- Enter a positive number.
- Optionally add a unit label like cm or m.
- Click Calculate to get side length, perimeter, area, apothem, and diagonals.
This is useful when you have partial design dimensions and need the complete geometry for cutting, drafting, pricing materials, or creating CAD references.
Core Formulas for a Regular Hexagon
1) Perimeter
If side length is s, then perimeter is:
P = 6s
2) Area
Because the hexagon is six equilateral triangles:
A = (3√3 / 2) s²
3) Apothem (Inradius)
The apothem is the distance from the center to the midpoint of a side:
a = (√3 / 2) s
4) Circumradius
The distance from the center to any vertex is:
R = s
5) Diagonals
- Long diagonal (opposite vertices): 2s
- Short diagonal (skip one vertex): √3·s
Worked Example
Suppose a regular hexagon has side length s = 10 cm.
- Perimeter: 6 × 10 = 60 cm
- Area: (3√3/2) × 100 ≈ 259.81 cm²
- Apothem: (√3/2) × 10 ≈ 8.66 cm
- Long diagonal: 2 × 10 = 20 cm
- Short diagonal: √3 × 10 ≈ 17.32 cm
Practical Uses
Architecture and Construction
Hexagonal layouts are used in pavers, decorative panels, skylight structures, and modular floor systems. Accurate area and perimeter values help estimate materials and labor.
Engineering and Manufacturing
Mechanical parts often use hex profiles (for example, nuts and tool interfaces). Radius and diagonal values can be critical for tolerance checks and fit.
Design, Games, and Mapping
Hex grids are common in board games and strategy maps because movement and adjacency remain visually balanced. Area scaling matters when creating map tiles at different sizes.
Common Mistakes to Avoid
- Using formulas for an irregular hexagon on a regular hexagon problem.
- Mixing units (for example, entering side in inches but interpreting area as square centimeters).
- Forgetting that area units are squared (cm², m², ft²).
- Rounding too early in multi-step calculations.
FAQ
Is this calculator for all hexagons?
No. It is for a regular hexagon only. Irregular hexagons need additional side lengths, angles, or coordinate geometry.
What if I only know area?
That works. Choose “Area” in the dropdown and the calculator will derive side length first, then compute all remaining properties.
Can I use decimal values?
Yes. Decimals are fully supported, which is useful for real-world fabrication and metric conversions.
Final Thoughts
A hexagon calculator saves time and reduces errors in planning, design, and analysis. With one known value, you can quickly get all essential dimensions—side, perimeter, area, apothem, and diagonals—without manually rearranging formulas every time.