Regular hexagons tile the plane with the shortest total edge length for a given area, which is why bees build hexagonal honeycombs. They appear in nuts and bolts, floor tiles, board games and carbon molecules.
How to use the Hexagon Calculator
- Side a
- Every result field is editable: type into Area or any other result and Side a plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
A regular hexagon splits into six equilateral triangles of side a, which gives all the formulas. Type into any result to find the side that produces it.
What each result means
- Area = 3×sqrt(3)÷2×[Side a]^2
- Perimeter = 6×[Side a]
- Long diagonal = 2×[Side a]
- Short diagonal = sqrt(3)×[Side a]
- Inradius (apothem) = sqrt(3)÷2×[Side a]
Example values
How the main result changes when Side a changes and everything else stays at the example values above:
| Side a (cm) | Area (cm²) |
|---|---|
| 2.5 | 16.238 |
| 3.75 | 36.5354 |
| 5 | 64.9519 |
| 6.25 | 101.4874 |
| 7.5 | 146.1418 |
| 10 | 259.8076 |
Formula
A = (3√3/2)·a², P = 6a, D = 2a, d = √3·a, R = a, r = (√3/2)·a
Worked example
Inputs — Side a: 5 cm.
Results — Area = 64.951905 cm²; Perimeter = 30 cm; Long diagonal = 10 cm; Short diagonal = 8.660254 cm; Circumradius = 5 cm; Inradius (apothem) = 4.330127 cm.
Key terms
- Regular hexagon
- A six-sided polygon with equal sides and angles.
Frequently asked questions
What is each interior angle of a hexagon?
120°.
Why do bees use hexagons?
They tile without gaps and use the least wax per stored volume.
How do I measure a hex nut?
Across flats is the short diagonal-direction width = √3·a; across corners = 2a.
How many diagonals does a hexagon have?
Nine: three long and six short.