Hexagon Calculator
How It Works
A regular hexagon has six equal sides and six equal angles of 120 degrees each. It is one of three regular polygons that can tessellate (tile a plane without gaps). The area formula is A = (3 sqrt 3 / 2) x s^2, where s is the side length.
A regular hexagon can be divided into six equilateral triangles, which makes many calculations straightforward. The apothem (distance from center to the middle of a side) equals s x sqrt(3)/2. The long diagonal (corner to opposite corner) equals 2s.
Hexagons appear throughout nature and engineering — from honeycomb cells to bolt heads to tiled floors. Their efficient packing ratio and structural strength make them popular in architecture and materials science.
Frequently Asked Questions
What is the area formula for a regular hexagon?
Area = (3√3/2) × s², where s is the side length. This equals approximately 2.598 × s². Alternatively, Area = (3√3/2) × s² ≈ 2.598s². For a hexagon with side 10, the area is about 259.8 square units.
How many diagonals does a hexagon have?
A regular hexagon has 9 diagonals total: 3 long diagonals connecting opposite vertices (length = 2s) and 6 short diagonals connecting vertices separated by one vertex (length = s√3).
What is the interior angle of a regular hexagon?
Each interior angle of a regular hexagon is 120 degrees. The sum of all interior angles is 720 degrees (calculated as (6-2) × 180°).
Why are hexagons common in nature?
Hexagons provide the most efficient way to divide a surface into equal areas with the minimum total perimeter. This is why bees use hexagonal cells — it minimizes the wax needed while maximizing storage space.