A regular hexagon has six equal sides and six 120° angles, and it is everywhere: honeycombs, floor tiles, nuts and bolts, pencils and snowflakes. Because it splits into six equilateral triangles, every measurement follows from the side length with a factor of √3. This calculator starts from whichever measurement you have, returns all the others with exact radical forms when possible, and draws the hexagon with its flats and corners labeled.
How to use the hexagon calculator
- Choose the measurement you know: side, width across flats, width across corners, apothem, perimeter or area.
- Enter its value and pick the unit.
- Read the area on the tape (or the side, if you started from the area), with every other measurement listed beneath. When your input is a simple number, exact forms such as 6√3 appear alongside the decimals.
Hexagon formulas
| Measurement | Formula in terms of side s |
|---|---|
| Circumradius (center to corner) | R = s |
| Apothem (center to side) | a = (√3/2)s ≈ 0.866s |
| Width across flats | F = √3 s ≈ 1.732s |
| Width across corners | C = 2s |
| Perimeter | P = 6s |
| Area | A = (3√3/2)s2 ≈ 2.598s2 |
Working backward:
The area can also be written as half the perimeter times the apothem, A = ½Pa, the general formula for any regular polygon.
Worked examples
Side 6 cm. Apothem 3√3 ≈ 5.196 cm; across flats 6√3 ≈ 10.392 cm; across corners 12 cm; perimeter 36 cm; area (3√3/2) × 36 = 54√3 ≈ 93.53 cm².
Check: six equilateral triangles of side 6 each have area (√3/4) × 36 ≈ 15.588 cm², and 6 × 15.588 ≈ 93.53 cm² ✓.
A hex nut. A 13 mm wrench fits a nut that is 13 mm across flats. Its side is 13 ÷ √3 ≈ 7.506 mm and its width across corners is about 15.01 mm — the clearance a socket must allow.
Hexagons in practice
Tiles and pavers
Only three regular polygons tile a floor on their own: triangles, squares and hexagons. To estimate how many hexagonal tiles cover a floor, divide the floor area by one tile’s area and add a waste allowance for cut edges, typically 10–15%.
Nuts, bolts and bar stock
Fastener sizes are specified across flats because that is where a wrench grips. Across-corners size matters for clearance: a socket or a recess must be at least 2/√3 ≈ 1.155 times the across-flats width.
Hexagonal prisms
A pencil, a nut or a column with a hexagonal cross-section is a hexagonal prism. Its volume is the hexagon’s area times the length, and its surface area is twice the hexagon’s area plus 6 × side × length.
Angles and symmetry
Each interior angle is 120° and the six angles add up to 720°. The exterior angles are 60°. A regular hexagon has six lines of symmetry and looks the same after a rotation of 60°, which is why it fits so naturally into patterns built from equilateral triangles.
Related tools
For polygons with any number of sides, use the regular polygon calculator. The octagon calculator covers eight-sided shapes such as stop signs, and the equilateral triangle calculator handles the triangles a hexagon is built from. The 2D shape formulas page collects area and perimeter rules for other figures.
Frequently asked questions
What is the area formula for a regular hexagon?
A = (3√3/2)s², where s is the side length. It comes from six equilateral triangles of side s, each with area (√3/4)s². A hexagon with 6 cm sides has area 54√3 ≈ 93.53 cm².
What is the difference between across flats and across corners?
Across flats is the distance between two opposite parallel sides, F = √3·s; across corners is the distance between opposite vertices, C = 2s. Wrench and socket sizes for hex nuts and bolts are measured across flats.
Is the side length equal to the radius?
Yes. In a regular hexagon the distance from the center to any corner (the circumradius) equals the side length, because the six triangles around the center are equilateral.
How many diagonals does a hexagon have?
Nine: six short diagonals that skip one vertex (each equal to √3·s, the across-flats width) and three long diagonals through the center (each 2s).
Why do bees use hexagons?
Regular hexagons tile a flat surface with no gaps and enclose the most area for a given perimeter among shapes that tile, so hexagonal cells use the least wax to store the most honey.