Hexagon Calculator

Calculate all properties of a regular hexagon including area, perimeter, apothem, circumradius, and diagonals. Ideal for honeycomb patterns, tiles, and engineering.

Length of one side of the regular hexagon

Area = (3sqrt3/2) * s^2 ≈ 2.598s^2 Perimeter = 6s Apothem = (sqrt3/2) * s ≈ 0.866s Circumradius = s (special property!) Long Diagonal = 2s Short Diagonal = sqrt3 * s ≈ 1.732s Interior Angle = 120deg Exterior Angle = 60deg Where: s = side length
Example 1 (Hex Tile): Side Length = 10 cm Area = 2.598 * 10^2 = 259.81 cm^2 Perimeter = 6 * 10 = 60 cm Apothem = 0.866 * 10 = 8.66 cm Circumradius = 10 cm Long Diagonal = 2 * 10 = 20 cm Short Diagonal = 1.732 * 10 = 17.32 cm Example 2 (Hex Bolt): Side Length = 8 mm Area = 2.598 * 8^2 = 166.27 mm^2 Perimeter = 6 * 8 = 48 mm Apothem = 0.866 * 8 = 6.93 mm Circumradius = 8 mm

What is a regular hexagon?

A regular hexagon is a six-sided polygon where all sides are equal in length and all interior angles are equal (120deg). Hexagons are common in nature (honeycomb), engineering (nuts and bolts), and design (floor tiles).

What is the formula for the area of a regular hexagon?

The area of a regular hexagon is: Area = (3sqrt3/2) * s^2 ≈ 2.598 * s^2, where s is the side length. Alternatively, it can be thought of as 6 equilateral triangles. For a hexagon with side 10 cm, area ≈ 2.598 * 100 = 259.81 cm^2.

How do I calculate the perimeter of a hexagon?

For a regular hexagon, the perimeter is: Perimeter = 6 * side length. For example, if each side is 5 cm, the perimeter is 6 * 5 = 30 cm. For irregular hexagons, add all six individual side lengths together.

What is the apothem of a hexagon?

The apothem is the distance from the center to the midpoint of any side, perpendicular to that side. For a regular hexagon: Apothem = (sqrt3/2) * s ≈ 0.866 * s, where s is the side length. The apothem is useful for area calculations.

What is special about the circumradius of a regular hexagon?

In a regular hexagon, the circumradius (radius of circumscribed circle) equals the side length! This unique property means if you draw a circle through all vertices, its radius is exactly equal to each side: Circumradius = s.

What are the interior and exterior angles of a regular hexagon?

Each interior angle of a regular hexagon is 120deg. Each exterior angle is 60deg. The sum of all interior angles is (6-2) * 180deg = 720deg. The 120deg angles make hexagons perfect for tessellation (tiling without gaps).

How many diagonals does a hexagon have?

A hexagon has 9 diagonals. Using the formula n(n-3)/2 where n=6: 6(6-3)/2 = 9 diagonals. There are 3 long diagonals passing through the center and 6 short diagonals connecting vertices two sides apart.

Why are hexagons so common in nature?

Hexagons are efficient for packing and use minimal material for maximum space. Honeybees use hexagonal cells because they provide the most storage with the least wax. This same efficiency makes hexagons ideal for engineering and design.

What are practical applications of hexagon calculations?

Hexagons are used in: honeycomb structures, hex bolts and nuts, tile patterns, game boards (hex grids), carbon molecular structures (graphene), pencil cross-sections, Giant's Causeway basalt columns, and soccer ball patterns.

How can I calculate a hexagon from the diameter?

If you know the diameter across opposite vertices (which equals 2 * side for a regular hexagon), divide by 2 to get the side length: s = diameter/2. Then use standard formulas to find area and perimeter.