⬡ Hexagon Calculator
Calculate properties of a regular hexagon
How to Use This Calculator
Enter Side Length
Input the length of one side of the regular hexagon.
Click Calculate
Press the "Calculate Hexagon Properties" button to compute all hexagon measurements.
Review Results
View the calculated area, perimeter, apothem, circumradius, and diagonal length.
Formula
Area = (3√3/2) × s²
Perimeter = 6s
Apothem = (√3/2) × s
Circumradius = s (for regular hexagon)
Where:
- s = Side length
- Apothem = Distance from center to midpoint of a side
- Circumradius = Distance from center to vertex
- For regular hexagon: circumradius = side length
Example: Calculate hexagon properties for side length = 10
Area = (3√3/2) × 10² = (3√3/2) × 100 = 150√3 ≈ 259.81 square units
Perimeter = 6 × 10 = 60 units
Apothem = (√3/2) × 10 = 5√3 ≈ 8.66 units
About Hexagon Calculator
The Hexagon Calculator helps you find the area, perimeter, apothem, and other properties of a regular hexagon. A regular hexagon has six equal sides and six equal angles (each 120°).
When to Use This Calculator
- Geometry: Calculate hexagon properties for geometric problems
- Engineering: Design hexagonal components, bolts, and mechanical parts
- Architecture: Calculate area and dimensions for hexagonal buildings or spaces
- Construction: Plan hexagonal structures, patios, or tiling
- Education: Learn and practice hexagon mathematics
- Design: Create hexagonal patterns, logos, or graphics
Why Use Our Calculator?
- ✅ Complete Properties: Calculates area, perimeter, apothem, and radius
- ✅ Instant Results: Get all hexagon measurements immediately
- ✅ Step-by-Step Display: See calculation formulas with your values
- ✅ Works with Any Units: Meters, feet, inches, or any unit
- ✅ 100% Accurate: Precise geometric calculations
- ✅ Completely Free: No registration required
Understanding Regular Hexagons
A regular hexagon is a six-sided polygon with all sides equal and all angles equal (120°). Key properties:
- Six Sides: All sides have equal length
- Six Angles: Each interior angle = 120° (sum = 720°)
- Equilateral Triangles: Can be divided into 6 equilateral triangles
- Tessellation: Hexagons can tile a plane perfectly (honeycomb pattern)
- Symmetry: Has 6-fold rotational symmetry
- Efficient Packing: Hexagonal arrangement is most efficient for packing circles
Real-World Applications
Honeycomb: Bees create hexagonal cells because hexagons use the least wax to create the most storage space. This is the most efficient shape for tiling.
Engineering: Hexagonal bolts and nuts are common because the hexagon shape provides good grip and is easy to manufacture. Many mechanical components use hexagonal designs.
Architecture: Hexagonal tiles are popular for flooring. The hexagonal shape creates interesting patterns and efficient use of space.
Chemistry: Many crystal structures have hexagonal arrangements. Carbon atoms in graphene form hexagonal lattices.
Frequently Asked Questions
What is a regular hexagon?
A regular hexagon is a six-sided polygon with all sides equal in length and all interior angles equal to 120°. It's a highly symmetric shape with 6-fold rotational symmetry.
How do you calculate hexagon area?
For a regular hexagon, area = (3√3/2) × s², where s is the side length. This formula comes from dividing the hexagon into 6 equilateral triangles.
What is the apothem of a hexagon?
The apothem is the distance from the center of the hexagon to the midpoint of any side. For a regular hexagon, apothem = (√3/2) × side length.
Why do bees use hexagonal cells?
Hexagons are the most efficient shape for tiling a plane with equal-sized cells. They use the least material (wax) while maximizing storage space, making them perfect for honeycomb construction.
Can hexagons tile a plane?
Yes! Regular hexagons are one of only three regular polygons that can perfectly tile a plane (along with squares and equilateral triangles). This is why they appear in honeycombs and many natural patterns.
What's the relationship between hexagon and equilateral triangle?
A regular hexagon can be divided into 6 equilateral triangles by drawing lines from the center to each vertex. Each triangle has side length equal to the hexagon's side length.
How many diagonals does a hexagon have?
A hexagon has 9 diagonals. The formula for diagonals in an n-sided polygon is n(n-3)/2. For hexagon: 6(6-3)/2 = 9.