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Calculators/Geometry/Hexagon
Geometry

Hexagon calculator

Area and perimeter of a regular hexagon from its side length, across-flats or across-corners measure.

What this calculator does

A regular hexagon is a six-sided shape with all sides and all interior angles equal, each interior angle measuring exactly 120°. It is one of the few regular polygons that tiles a flat plane with no gaps, which is why it turns up in honeycomb, floor tiles and hex-head fasteners alike.

This hexagon calculator accepts whichever measurement is easiest to take: the side length itself, the across-flats distance between two opposite sides (the size a spanner or socket is specified by), or the across-corners distance between two opposite points.

The formula

FormulaArea = (3√3/2) × s²

Area of a regular hexagon is (3√3/2) × s², where s is the side length. If you measured across the flats instead (the perpendicular distance between two opposite sides), the side length is that value divided by √3; if you measured across the corners (the distance between two opposite vertices), the side length equals half of that.

TermMeaning
sSide length of the regular hexagon.
Across flatsThe perpendicular distance between two opposite sides, equal to s√3.
Across cornersThe distance between two opposite vertices, equal to 2s.

The inputs explained

FieldWhat to enter
ValueEnter the side length, across-flats distance, or across-corners distance.
This value is theSelect which measurement the value above represents.

When to use it

Sizing a hex bolt, nut or socket

Hex fasteners are specified by their across-flats size, the dimension a spanner or socket needs to match; converting that to a side length or across-corners size checks clearance in a tight space.

Laying hexagon floor or wall tiles

Hexagon tiles are usually sold by their across-flats or side measurement; the area of one tile, from this hexagon calculator, multiplied by the number of tiles, estimates total coverage.

Working out honeycomb or mesh cell area

Hexagonal cells in honeycomb structures, mesh or packaging fill material are close to regular hexagons, and their area follows the same hexagon formula from the cell’s side length.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

Hexagon formula: how area and perimeter change with side length

The area and perimeter of a regular hexagon across a range of side lengths.

Area and perimeter across a range of side lengths
Side lengthAreaPerimeter
210.39212.000
564.95230.000
10259.80860.000
15584.56790.000
201,039.23120.000
302,338.27180.000
Perimeter grows in direct proportion to the side length, since it is simply six times the side; area grows with the square of the side length, so it accelerates away from perimeter as the hexagon gets larger.

Side length, across flats or across corners: does it matter which you enter?

The same physical hexagon (side length 10) entered as a side length, and again using its across-flats and across-corners measurements, to confirm the hexagon calculator returns the same shape either way.

A side-10 hexagon entered three different ways
The value entered is theAreaSide length
Side length (10)259.80810.000
Across flats (17.32)86.6035.774
Across corners (20)64.9525.000
All three rows describe the same side-10 hexagon, so the area and recovered side length come out the same regardless of which measurement was actually entered.

Questions

What is the hexagon formula for area?

Area = (3√3/2) × s², where s is the side length of a regular hexagon. The constant 3√3/2 is approximately 2.598.

What is a hexagon?

A hexagon is any six-sided polygon. A regular hexagon has all six sides and all six interior angles equal, with each interior angle measuring exactly 120°.

What does "across flats" mean on a hexagon?

Across flats is the perpendicular distance between two opposite (parallel) sides of the hexagon, the dimension used to size a spanner, socket or hex-head bolt. It is smaller than the across-corners measurement.

How many sides does a hexagon have and what are its angles?

A hexagon has six sides. In a regular hexagon, each interior angle is 120°, and the six interior angles sum to 720°.

For any regular polygon with a different number of sides, see the full regular polygon calculator. For a six-sided shape built from triangles instead, see the triangle area calculator.