Hexagon Area Calculator
A regular hexagon is a six-sided polygon with all sides of equal length and all interior angles of 120 degrees. This calculator computes the area, perimeter, circumradius, and apothem of a regular hexagon from the side length. The area formula equals (3 * sqrt(3) / 2) times the square of the side length, or approximately 2.59808 times the side length squared. The perimeter is simply six times the side length. A unique property of the hexagon is that its circumradius (radius of the circumscribed circle) equals its side length. The apothem (radius of the inscribed circle) equals sqrt(3)/2 times the side length. Regular hexagons are the most efficient shapes for tiling and packing, which is why they appear in honeycomb structures.
Hexagon formulas
Area = (3 * sqrt(3) / 2) * s^2
Area (approximate) = 2.59808 * s^2
Perimeter = 6 * s
Circumradius (R) = s
Apothem (a) = (sqrt(3) / 2) * s
Apothem (approximate) = 0.86603 * s
Example calculation
For a regular hexagon with side length 10:
- Area = 2.59808 * 10^2 = 259.81 square units
- Perimeter = 6 * 10 = 60 units
- Circumradius = 10 units
- Apothem = 0.86603 * 10 = 8.66 units
Hexagon area calculator: frequently asked questions
What is a regular hexagon?
A regular hexagon is a six-sided polygon with all sides of equal length and all interior angles equal to 120 degrees. It is one of the most common regular polygons in nature, appearing in honeycomb structures and mineral formations.
What is the formula for the area of a regular hexagon?
The area of a regular hexagon with side length s is: Area = (3 * sqrt(3) / 2) * s^2, which simplifies to approximately 2.59808 * s^2. A hexagon can be divided into six equilateral triangles from the center.
Why are hexagons common in nature?
Hexagons are the most efficient shape for tiling and packing, requiring the least perimeter for a given area. Honeybees use this principle to build hexagonal honeycomb cells, and this shape appears in basalt columns, snowflakes, and other natural structures.
What are the interior angles of a regular hexagon?
Each interior angle of a regular hexagon is 120 degrees. The sum of all six interior angles is 720 degrees, which follows the formula (n-2)*180 for an n-sided polygon.
What are the circumradius and apothem of a hexagon?
For a regular hexagon, the circumradius equals the side length (R = s). The apothem equals (sqrt(3)/2) * s, or approximately 0.86603 * s. This is unique among regular polygons.
Official sources
- Wolfram MathWorld: Regular Hexagon.
- ISO 80000-2: Mathematical signs and symbols.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.