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Hexagon Area Calculator

Regular hexagon area from its side — A = (3√3/2)·s².

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How to use

  1. 1.Enter the side length (s) — the length of one edge of the regular hexagon — in any unit.
  2. 2.The calculator instantly applies A = (3√3/2)·s² and shows the worked formula.
  3. 3.Read the hexagon area below, along with the perimeter (6·s), apothem (√3/2·s), and circumradius (s).

About Hexagon Area Calculator

The area of a hexagon (regular) is A = (3√3/2)·s², where s is the length of one side. This hexagon area calculator returns that value the instant you type the side length, and it also gives the perimeter, the apothem (the inradius), and the circumradius — so you can describe the whole six-sided shape from a single number.

Why this formula works is easy to picture: a regular hexagon splits neatly into six identical equilateral triangles that all meet at the center. Each equilateral triangle of side s has area (√3/4)·s², and six of them give 6 × (√3/4)·s² = (3√3/2)·s² ≈ 2.598076·s². That is the whole trick — the hexagon is the friendliest regular polygon precisely because it tiles into equilateral triangles with no leftover pieces. The tool uses the exact value of √3 (not a rounded 1.732) so the result stays accurate to many decimal places.

Alongside the area you get three more measurements. The perimeter is simply 6·s, since all six edges are equal. The apothem — the distance from the center to the midpoint of a side, and the radius of the largest circle that fits inside — is (√3/2)·s ≈ 0.8660254·s. The circumradius R, the distance from the center to any corner and the radius of the circle that passes through every vertex, equals the side length exactly: R = s. That last identity is special to the regular hexagon and is the reason a hexagon fits perfectly around a circle of radius s.

The area comes out in square units of whatever unit you used for the side. Keep the side in one unit and the result is that unit squared — centimeters give square centimeters, meters give square meters, inches give square inches. The tool never converts units for you, so the math stays exactly (3√3/2)·s².

Hexagon area shows up everywhere. Hex nuts and bolt heads are measured across their flats, which is twice the apothem, so their reach is the circumradius s; honeycomb and hexagonal tiling use the six-triangle structure because hexagons cover a plane with the least perimeter per unit area, which is why bees build them and why floor tiles, board-game maps, chicken wire, graphene, and pencil cross-sections are hexagonal. Engineers, machinists, tilers, quilters, and students across geometry and trigonometry all need this number. Everything here runs locally in your browser — nothing is uploaded — so results are instant and private.

A quick worked example: with s = 2, the area is (3√3/2)·4 = 6√3 ≈ 10.3923 square units, the perimeter is 12, the apothem is √3 ≈ 1.7320508, and the circumradius is 2.

Frequently asked questions

What is the formula for the area of a hexagon?
For a regular hexagon the area is A = (3√3/2)·s², where s is the side length. That constant, 3√3/2, is about 2.598076, so the area is roughly 2.598076 times the side squared. For example, s = 2 gives (3√3/2)·4 = 6√3 ≈ 10.3923 square units. The formula comes from splitting the hexagon into six equilateral triangles.
Why is a hexagon six equilateral triangles?
Drawing lines from the center to each of the six corners cuts a regular hexagon into six triangles that are all equilateral with side s. Each has area (√3/4)·s², so six of them give 6 × (√3/4)·s² = (3√3/2)·s². This clean split is unique to the regular hexagon and is why its area formula is so simple.
What is the apothem of a hexagon?
The apothem is the distance from the center to the midpoint of a side — the radius of the inscribed circle. For a regular hexagon it is (√3/2)·s ≈ 0.8660254·s. Twice the apothem is the width across the flats, which is how hex nuts and wrench sizes are measured. For s = 2 the apothem is √3 ≈ 1.7320508.
Why does the circumradius of a hexagon equal its side length?
The circumradius R is the distance from the center to a corner. Because a regular hexagon is made of six equilateral triangles meeting at the center, each triangle's two center-to-corner edges are equal to its base, the side s. So R = s exactly — a property unique to the regular hexagon, which is why a hexagon fits snugly around a circle of radius s.
What units does the hexagon area come out in?
It is unit-agnostic. Enter the side in any unit and the area is that unit squared: centimeters give square centimeters, meters give square meters, inches give square inches. The tool does not convert units, so keep the side in one consistent unit and the (3√3/2)·s² result stays exact.

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