Regular Hexagon Calculator
Enter one known value for a regular hexagon and this calculator will find the rest.
Assumes a regular hexagon (all sides and interior angles equal).
What is a regular hexagon?
A hexagon is a six-sided polygon. In geometry, the most common type used in calculations is the regular hexagon, where all six sides have equal length and each interior angle is 120°. You see this shape everywhere: honeycombs, tile patterns, nuts and bolts, logos, and even board games with hex maps.
The reason regular hexagons are so practical is simple: once you know one measurement, you can derive almost every other measurement using clean formulas. That makes them ideal for design, architecture, fabrication, and classroom geometry.
Core hexagon formulas
Let s be the side length. These are the formulas used in the calculator:
Area: A = (3√3 / 2) s²
Apothem (inradius): a = r = (√3 / 2) s
Circumradius: R = s
Long diagonal: dlong = 2s
Short diagonal: dshort = s√3
The calculator first converts your input into side length s, then computes all other values from that base.
How to use this calculator
- Select which value you already know (side, area, perimeter, diagonal, etc.).
- Enter the numeric value.
- Optionally set a unit (for example, cm or m).
- Choose decimal precision and click Calculate.
If your unit is linear (like cm), area is returned in square units (cm²). If no unit is entered, the result displays plain numbers.
Example calculation
Given side length = 10 cm
If s = 10, then:
- Perimeter = 6 × 10 = 60 cm
- Area = (3√3 / 2) × 10² ≈ 259.8076 cm²
- Apothem = (√3 / 2) × 10 ≈ 8.6603 cm
- Long diagonal = 20 cm
- Short diagonal ≈ 17.3205 cm
This is exactly the kind of multi-value output the tool gives instantly from one input.
Common mistakes to avoid
- Using irregular hexagon dimensions: this tool is for regular hexagons only.
- Mixing units: keep all measurements in the same unit system.
- Confusing diagonals: long diagonal is 2s, short diagonal is s√3.
- Rounding too early: keep extra decimal places while working, then round at the end.
Where hexagon math is useful
Hexagon calculations are useful in a surprising number of areas:
- Flooring and tiling layout estimates
- Mechanical design (hex features and cutouts)
- 3D printing and laser cutting templates
- Game map design with hex grids
- Educational geometry practice
If you frequently work with six-sided geometry, a fast calculator like this can save time and reduce manual errors.