How this calculator works
A regular hexagon has six equal sides and six equal angles. It can be split into six equilateral triangles meeting at the centre, which is why the circumradius, the distance from the centre to a vertex, equals the side length. The apothem, the perpendicular distance from the centre to a side, is √3/2 times the side. Those relationships make every other property a simple multiple of the side, so entering the area, perimeter, a radius or a diagonal first recovers the side and then builds the rest.
Formula
Side a. Perimeter = 6a. Area = (3√3/2)a². Apothem = (√3/2)a. Circumradius = a. Short diagonal = √3a. Long diagonal = 2a.
Worked example
A hexagon with side 10 m has perimeter 60 m, area (3√3/2) × 100 ≈ 259.8076 m², apothem 5√3 ≈ 8.6603 m, short diagonal 10√3 ≈ 17.3205 m and long diagonal 20 m.
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Frequently asked questions
Why does the circumradius equal the side?
The six triangles from the centre to the vertices are equilateral, so each has all three sides equal. One side is a hexagon edge and the other two are radii.
What is the difference between the short and long diagonal?
The short diagonal skips one vertex and has length √3a. The long diagonal passes through the centre and joins opposite vertices, so it is a diameter of the circumscribed circle, 2a.
Can I use the apothem instead?
This calculator does not ask for the apothem directly. Recover the side with a = 2 × apothem / √3, then enter that side.
Is a honeycomb cell a regular hexagon?
Each cell in a honeycomb is close to a regular hexagon. Real cells have slightly thicker walls at the corners, but the idealised geometry here is the usual model for them.