Hexagon Calculator
Area, perimeter and apothem of a regular hexagon.
Area
64.9519
regular hexagon
Perimeter
30
Apothem
4.3301
Long diagonal
10
AI Breakdown & Smart Takeaway
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How the Hexagon Calculator works
The GKCalculators Hexagon Calculator instantly computes the area, perimeter, and apothem of any regular hexagon from a single input — the side length. It's ideal for students, architects, engineers, tile designers, and hobbyists who need precise hexagonal geometry without manual calculation.
A regular hexagon is a six-sided polygon where every side is equal in length and every interior angle measures exactly 120°. What makes the regular hexagon uniquely powerful in geometry is that it can be divided into six equilateral triangles, all sharing a common center point. This internal symmetry is the foundation of every formula this calculator uses — once you know just the side length, every other meaningful measurement follows directly from it.
The calculator derives three key outputs from your side length input. The perimeter is the simplest: multiply the side length by 6, since all six sides are identical. The area is computed using the formula A = (3√3 / 2) × s², which emerges naturally from summing the areas of those six equilateral triangles. The apothem — the perpendicular distance from the center of the hexagon to the midpoint of any side — is calculated as a = (√3 / 2) × s, and it represents the inradius of the hexagon. All three results update simultaneously, so you can see how they relate to each other at a glance.
A common mistake is confusing the apothem with the circumradius. The circumradius (R) is the distance from the center to a vertex, and for a regular hexagon it equals the side length exactly (R = s). The apothem, by contrast, is always shorter than the circumradius by a factor of √3/2 (approximately 0.866). When measuring a physical hexagon — such as a hex bolt, a tile, or a honeycomb cell — it's easy to accidentally measure the flat-to-flat distance (which is 2 × apothem) rather than the corner-to-corner distance (which is 2 × circumradius). Inputting the wrong measurement will skew all your results, so always confirm which dimension you actually have.
For real-world applications like tiling or material estimation, the area formula is your most critical output. Because hexagonal tiling covers a plane with zero gaps and no overlaps, the area of each tile directly tells you how many tiles you need for a given surface — simply divide total surface area by one tile's area and add a 5–10% buffer for cuts and waste. Architects and game designers also use the apothem when spacing hexagonal grids, since it determines the center-to-center distance between adjacent cells in a honeycomb arrangement.
Formula
Area = (3√3 / 2)·s²
Pro tips
- If you have a flat-to-flat measurement (common on hex bolts and nuts), divide it by √3 to get the side length before entering it into the calculator.
- If you measured corner-to-corner (vertex to vertex), simply use that measurement directly as the side length — for a regular hexagon, the circumradius equals the side length.
- When estimating materials for hexagonal tiling, always add at least 10% to the calculated area to account for edge cuts, especially on irregular room boundaries.
- For honeycomb or grid-based designs, the center-to-center spacing between adjacent hexagons equals 2 × apothem (flat-to-flat) or √3 × s — the calculator's apothem output makes this trivial to find.
- Double-check your units before inputting: if your side length is in centimeters, your area result will be in cm² and your perimeter in cm — mixing inches and centimeters is the most frequent source of real-world errors.
Key terms
- Side Length (s)
- — The length of one edge of the regular hexagon; since all six sides are equal, this single value defines the entire shape.
- Apothem
- — The perpendicular distance from the center of the hexagon to the midpoint of any side, also called the inradius; equal to (√3 / 2) × s.
- Circumradius
- — The distance from the center of the hexagon to any vertex; uniquely, for a regular hexagon this equals the side length exactly.
- Perimeter
- — The total length of all six sides of the hexagon, calculated simply as 6 times the side length.
- Area
- — The total surface enclosed by the hexagon, given by (3√3 / 2) × s², derived by treating the hexagon as six congruent equilateral triangles.
- Regular Hexagon
- — A hexagon in which all six sides are equal in length and all six interior angles each measure 120°, making it perfectly symmetric.
