Understand the regular hexagon

A regular hexagon has six equal sides and six equal angles. Its centre divides it into six equilateral triangles. This special structure makes its circumradius exactly equal to its side length.

Properties that make the calculations work

Every interior angle is 120 degrees. The distance across opposite vertices is 2a, while the distance across opposite parallel sides is √3a. Its apothem is √3a/2.

Where the model is useful

The side and radius tools support tile layouts and idealised hexagonal drawings. Real nuts, honeycomb walls and material patterns have thickness, clearance and manufacturing conventions beyond a pure polygon.

Measure the right thing

The circumradius equals a side only for the regular hexagon, not for all regular polygons.

Sketch the figure and mark every known measurement before choosing a calculator. A length measured along an edge is not automatically a perpendicular height. If a formula needs a radius, check that the value has not been measured across a full diameter. Write the unit beside each known quantity before entering it.

Scale and units

Multiplying every length by k multiplies any area by k². This is a useful check: doubling all dimensions cannot merely double an area. Inputs expressed in centimetres produce cm² for area; the unit selector relabels rather than converts entered numbers.

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Wolfram MathWorld: Regular hexagon provides reference reading. Our summaries and examples are written for this portal and are not a specialist-reviewed textbook. Try a worked example or suggest a correction.