Hexagon Calculator
Calculate area, perimeter, diagonals, and other properties of regular hexagons
Calculate Hexagon Properties
Choose which measurement you know to calculate all other properties
Enter a positive value to calculate all hexagon properties
Hexagon Properties
Regular Hexagon Diagram
Example Calculation
Regular Hexagon with Side Length 10 units
Given: Side length (a) = 10 units
Area: (3√3/2) × 10² = (3√3/2) × 100 ≈ 259.81 square units
Perimeter: 6 × 10 = 60 units
Long diagonal: 2 × 10 = 20 units
Short diagonal: √3 × 10 ≈ 17.32 units
Apothem: (√3/2) × 10 ≈ 8.66 units
Hexagon Properties
Sides
A hexagon has exactly 6 sides
Diagonals
3 long diagonals + 6 short diagonals
Interior Angle
Each interior angle = 120°
Sum of Angles
Total interior angles = 720°
Hexagon Facts
Regular hexagons tessellate perfectly (no gaps)
Found in nature: honeycombs, snowflakes, crystals
Circumradius equals the side length
Can be divided into 6 equilateral triangles
Most efficient shape for covering area
Understanding Regular Hexagons
What is a Regular Hexagon?
A regular hexagon is a 6-sided polygon where all sides have equal length and all interior angles are equal (120°). It's one of the most efficient shapes in nature and mathematics.
Key Properties
- •Sides: 6 equal sides
- •Interior angles: Each 120°, sum = 720°
- •Diagonals: 9 total (3 long, 6 short)
- •Symmetry: 6-fold rotational and reflectional
Hexagon Formulas
Area: A = (3√3/2) × a² ≈ 2.598 × a²
Perimeter: P = 6a
Long diagonal: D = 2a
Short diagonal: d = √3 × a ≈ 1.732a
Apothem: r = (√3/2) × a ≈ 0.866a
Note: Where 'a' represents the side length of the regular hexagon.
Types of Diagonals
Long Diagonals
Pass through the center, connect opposite vertices. Length = 2a. There are 3 long diagonals.
Short Diagonals
Don't pass through center, skip one vertex. Length = √3 × a. There are 6 short diagonals.