Regular Hexagon Calculator
Choose one known measurement, enter its value, and calculate all major properties of a regular hexagon instantly.
Why a Hexagon Calculator Is Useful
A regular hexagon appears everywhere: honeycomb structures, tile layouts, nuts and bolts, game maps, logos, and architecture. Because all six sides and interior angles are equal, a regular hexagon is one of the most practical polygons for design and engineering.
The challenge is that you may only know one measurement—like area or perimeter—but still need everything else. This calculator solves that by converting your known value into side length first, then deriving every other property.
Core Formulas for a Regular Hexagon
Let s be side length. These are the key relationships used in the calculator:
- Perimeter: P = 6s
- Apothem (inradius): a = (√3 / 2)s
- Area: A = (3√3 / 2)s²
- Circumradius: R = s
- Long diagonal: dₗ = 2s
- Short diagonal: dₛ = √3s
Once you know one dimension, these formulas make the rest straightforward.
How to Use This Calculator
1) Select your known value type
Use the dropdown to choose the dimension you already have: side, perimeter, apothem, area, circumradius, or one of the diagonals.
2) Enter the value
Type a positive number. Decimals are supported. For area, enter square units as a plain number (for example, 240.5).
3) Add a unit label (optional)
If you enter cm, the calculator will display linear results in cm and area in cm².
4) Click Calculate
You will see all major geometric properties in one result panel, plus the conversion formula used to derive side length.
Worked Examples
Example A: Given side length
Suppose s = 10 cm.
- Perimeter: 60 cm
- Apothem: 8.6603 cm
- Area: 259.8076 cm²
- Long diagonal: 20 cm
- Short diagonal: 17.3205 cm
Example B: Given area
Suppose A = 150 m². Rearranging area formula:
s = √(2A / (3√3))
After finding s, all other values follow directly using the standard equations.
Practical Uses in Real Projects
- Flooring and tile planning: estimate material quantities and border lengths.
- Mechanical design: convert across flats/diagonals for hex components.
- 3D modeling and CAD: quickly set accurate dimensions from one known constraint.
- Education: verify classroom geometry work and check algebraic manipulation.
- Game development: size hex-grid cells consistently for maps and board mechanics.
Common Mistakes to Avoid
- Mixing unit systems (for example, entering inches and reading output as millimeters).
- Entering negative or zero values for geometric lengths.
- Confusing apothem (center to side midpoint) with circumradius (center to vertex).
- Treating arbitrary six-sided shapes as regular hexagons. These formulas require equal sides and equal angles.
Quick Reference
If you remember only one thing, remember this: in a regular hexagon, side length equals circumradius. That single insight makes many conversions faster and easier.
Use the calculator above whenever you need accurate hexagon dimensions for design, budgeting, fabrication, or study.