Hexagon calculator
A regular hexagon with sides of 6 has an area of 93.5307, an apothem of 5.19615 and 120° corners in the hexagon calculator.
Area
- Side length
- 6
- Apothem (inradius) The distance from the center to the middle of a side, and the radius of the largest circle inside.
- 5.19615
- Circumradius The distance from the center to a corner, and the radius of the circle through every corner.
- 6
- Perimeter
- 36
- Interior angle
- 120°
- Exterior angle
- 60°
- Sum of the interior angles
- 720°
- Diagonals
- 9
- Working
- Area = ½ × perimeter × apothem = ½ × 36 × 5.19615 = 93.5307
- Width across the flats Twice the apothem: the size a hex nut or bolt head is given by.
- 10.3923
- Width across the corners
- 12
How the Regular Polygon Calculator works
A regular hexagon is six equilateral triangles meeting at the center, each with sides equal to the hexagon's side s. That makes the circumradius equal to s, and the apothem the height of one triangle, (√3 ÷ 2) × s.
The area formula for a hexagon is six of those triangles: area = 6 × (√3 ÷ 4) × s² = (3√3 ÷ 2) × s², or about 2.598076 × s².
Worked example, a hexagon with sides of 6: the apothem is 0.866025 × 6 = 5.19615, the area is 2.598076 × 36 = 93.5307, which is exactly 54√3, and the perimeter is 36.
A hexagon has two widths. Across the flats it is twice the apothem, √3 × s = 10.3923 for a side of 6; across the corners it is twice the side, 12. A hex nut or bolt head is sized across the flats, so a 10 mm wrench fits a hexagon with an apothem of 5 mm and sides of 5.7735 mm.
Each interior angle is 120°, and the six total 720°. Three hexagons meet at every corner of a honeycomb or a tiled floor because 3 × 120° = 360°, which makes the hexagon one of only three regular polygons that tile a flat surface, with the triangle and the square.
Regular Polygon Calculator FAQ
How do I find the area of a hexagon from the width across the flats?
Halve the width to get the apothem, then the side is the apothem × 2 ÷ √3. A hexagon 10 across the flats has an apothem of 5, a side of 5.7735 and an area of 86.6025.
How many diagonals does a hexagon have?
Nine: 6 × 3 ÷ 2. Three are long diagonals through the center, each twice the side, and six are short ones, each √3 × the side.
How do I cut a hexagon from a circle?
Set a compass to the circle's radius and step it around the edge; it marks six corners exactly, because the hexagon's side equals the circumradius.