Hexagon Calculator
Calculate area, perimeter, diagonals, apothem, and radii from any known value
Input Values
How to Use the Hexagon Calculator
- Select Input Type: Choose whether to calculate from side, area, perimeter, diagonal, or apothem
- Enter Value: Input the known measurement
- View Results: All properties are calculated instantly including area, perimeter, diagonals, and radii
- Copy Values: Click the copy button next to any result
Understanding Regular Hexagons
A regular hexagon is a six-sided polygon with all sides equal in length and all interior angles equal (120° each). It has remarkable mathematical properties and is found throughout nature and human design.
Key Properties:
- 6 equal sides and 6 equal angles
- Interior angle: 120° each
- Sum of angles: 720°
- 9 diagonals (3 long + 6 short)
- 6-fold rotational symmetry
- 6 lines of symmetry
- Circumradius = Side length (unique property)
Perfect Tessellation:
The hexagon is one of only three regular polygons that can tile a plane with no gaps (along with triangles and squares). This makes it the most efficient shape for dividing a surface into equal areas with the minimum total perimeter.
Hexagon Formulas
Basic Formulas
Radius & Apothem
Practical Applications
Nature
- Honeycomb cells (bee hives)
- Snowflake crystals
- Basalt columns (Giant's Causeway)
- Turtle shell patterns
- Compound eyes of insects
Engineering & Design
- Hex bolts and nuts
- Honeycomb structures (aerospace)
- Floor tiles and paving
- Game boards (strategy games)
- Solar panel arrangements
Architecture
- Pavilions and gazebos
- Window designs
- Building floor plans
- Decorative patterns
Science & Technology
- Graphene structure
- Carbon nanotubes
- Benzene ring (organic chemistry)
- Saturn's hexagonal storm
Frequently Asked Questions
How do I find the area of a regular hexagon?
Use A = (3√3/2) × s² ≈ 2.598 × s², where s is the side length. Alternatively, A = (1/2) × Perimeter × Apothem.
Why is the circumradius equal to the side length?
A regular hexagon can be divided into 6 equilateral triangles. Each triangle has the same side length as the hexagon, and the circumradius equals this side length.
Why are hexagons so common in nature?
Hexagons are the most efficient shape for tessellation, maximizing area while minimizing perimeter. This makes them optimal for structures like honeycombs where efficiency matters.
How many diagonals does a hexagon have?
A hexagon has 9 diagonals: 3 long diagonals that pass through the center, and 6 short diagonals. Formula: n(n-3)/2 = 6(3)/2 = 9.