Calculate all properties of a regular hexagon from side length, area, perimeter, apothem, or circumradius. Includes area, perimeter, apothem, diagonals, circumradius, inradius, and angles.
The regular hexagon — a six-sided polygon with all sides and angles equal — is one of nature's favorite shapes. Honeybees build hexagonal cells because hexagons tile a plane with zero wasted space while minimizing wall material. The same efficiency makes hexagons popular in engineering, architecture, board games, and even traffic signs (the octagonal stop sign's close cousin).
A regular hexagon can be divided into exactly six equilateral triangles, all sharing a vertex at the center. This elegant decomposition gives rise to its key formulas: Area = (3√3/2)s², Perimeter = 6s, and a remarkable property — the circumradius (center-to-vertex distance) equals the side length itself. The apothem (center-to-side-midpoint distance, also the inradius) is s√3/2.
Hexagons have 9 diagonals: 3 "long" diagonals of length 2s pass through the center, and 6 "short" diagonals of length s√3 connect vertices separated by one vertex. Each interior angle is 120°, and each central angle is 60°.
This calculator works in reverse too — enter the area, perimeter, apothem, or circumradius, and it derives the side length and all other properties. Presets for real-world hexagons (honeycomb cells, hex bolts, stop signs, board game tiles) let you explore instantly. Whether you're designing a hexagonal patio, analyzing crystal structures, or just curious, this tool covers every property of the regular hexagon.
The Regular Hexagon Calculator — Area, Perimeter, Diagonals is useful when you need fast and consistent geometry results without reworking the same algebra repeatedly. It helps you move from raw measurements to Side Length, Area, Perimeter in one pass, with conversions and derived values shown together.
Use it to validate homework steps, check CAD or fabrication dimensions, estimate material requirements, and sanity-check hand calculations before submitting work.
Area: A = (3√3/2)s² Perimeter: P = 6s Apothem (inradius): a = (s√3)/2 Circumradius: R = s Short diagonal: d₁ = s√3 Long diagonal: d₂ = 2s Interior angle: 120° Central angle: 60° Number of diagonals: 9
Result: Area ≈ 64.95 cm², Perimeter = 30 cm, Apothem ≈ 4.33 cm
For a regular hexagon with side 5 cm: Area = (3√3/2) × 25 ≈ 64.95 cm². Perimeter = 6 × 5 = 30 cm. Apothem = 5 × √3/2 ≈ 4.33 cm. Circumradius = 5 cm (equals side length). Short diagonal = 5√3 ≈ 8.66 cm. Long diagonal = 10 cm.
This calculator combines the core geometry formula with the input mode selected in the interface, then derives companion values shown in the output cards, comparison bars, and reference tables. Use it to cross-check both direct calculations and reverse-solving scenarios where one measurement is unknown.
Regular Hexagon Calculator — Area, Perimeter, Diagonals calculations show up in coursework, drafting, construction layout, packaging, tank sizing, machining, and quality control. Instead of solving each transformation manually, you can test scenarios quickly and verify whether your dimensions remain within tolerance.
Keep units consistent across every input before interpreting area, perimeter, angle, or volume outputs. For best results, measure carefully, round only at the final step, and compare at least one manual calculation with the calculator output when building confidence.
A = (3√3/2)s², where s is the side length. For side 10: A = (3√3/2) × 100 ≈ 259.81 square units.
The apothem is the perpendicular distance from the center to the midpoint of a side. For a regular hexagon, it's (s√3)/2 and equals the inradius.
A regular hexagon is composed of 6 equilateral triangles. Each triangle has the same side length as the hexagon, and the circumradius is one side of those triangles.
9 diagonals total: 3 long diagonals (2s) that pass through the center, and 6 short diagonals (s√3) that don't. Understanding this concept helps you apply the calculator correctly and interpret the results with confidence.
Hexagons are the most efficient shape for tiling a plane — they cover area with the least perimeter (wall material). This was conjectured in 36 BC and proven mathematically in 1999 (Honeycomb Conjecture).
No, US stop signs are regular octagons (8 sides). But many nuts, bolts, and hex keys are hexagonal due to their efficient grip geometry.