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

0.000
Side Length
0.000
Area
0.000
Perimeter
0.000
Long Diagonal
0.000
Short Diagonal
0.000
Circumradius
0.000
Apothem
120°
Interior Angle
60°
Exterior Angle

Regular Hexagon Diagram

Side (a)ApothemShort DiagonalLong DiagonalCenter

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

6

Sides

A hexagon has exactly 6 sides

9

Diagonals

3 long diagonals + 6 short diagonals

120°

Interior Angle

Each interior angle = 120°

720°

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.

Real-World Applications

🐝Honeycombs: Bees use hexagonal cells for maximum efficiency
❄️Snowflakes: Natural hexagonal crystal structure
🏗️Engineering: Hexagonal tiles, nuts, bolts
🔬Chemistry: Benzene rings, carbon structures
🎮Games: Board games, tile-based strategy games