Hexagon Calculator (Regular)
Enter any one known value of a regular hexagon — side, circumradius, apothem, flat-to-flat width, point-to-point height, or even area — and this tool will compute everything else. Optionally, add height to get the volume of a hexagonal prism.
any unit
for hexagonal prism volume
Hexagon formulas
Regular hexagon basics
Perimeter: \(P = 6a\)
Area: \(A = \frac{3\sqrt{3}}{2} a^2\)
Apothem (inradius): \(r = \frac{\sqrt{3}}{2} a\)
Circumradius: \(R = a\)
Flat-to-flat width (distance between opposite sides): \(w = 2r = \sqrt{3} a\)
Point-to-point height (distance between opposite vertices): \(h = 2R = 2a\)
From area to side: \(a = \sqrt{\frac{2A}{3\sqrt{3}}}\)
Hexagonal prism volume (base = regular hex): \(V = A \cdot h_{prism}\)
FAQs
Can I use this for beehive / tiling hexagons?
Yes — those are typically regular hexagons defined by flat-to-flat size. Use the “By flat-to-flat” tab.
What if my hexagon is irregular?
This tool is for regular hexagons. For irregular ones, you need a polygon-area method with all vertex coordinates.
Why is circumradius = side for regular hexagons?
A regular hexagon can be inscribed in a circle of radius equal to its side length, because it is made of 6 equilateral triangles.
Formula (LaTeX) + variables + units
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Regular hexagon basics Perimeter: \(P = 6a\) Area: \(A = \frac{3\sqrt{3}}{2} a^2\) Apothem (inradius): \(r = \frac{\sqrt{3}}{2} a\) Circumradius: \(R = a\) Flat-to-flat width (distance between opposite sides): \(w = 2r = \sqrt{3} a\) Point-to-point height (distance between opposite vertices): \(h = 2R = 2a\) From area to side: \(a = \sqrt{\frac{2A}{3\sqrt{3}}}\) Hexagonal prism volume (base = regular hex): \(V = A \cdot h_{prism}\)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.