Area of a Regular Hexagon Calculator

Enter side length, apothem, or area — instantly get all regular hexagon properties with step-by-step working.

Unit:
Side (s)
cm
Apothem (a)
cm
Area (A)
cm²

💡 Enter any one value — the others update instantly.

Regular Hexagon Diagram

Regular Hexagon Formulas

From Side

A = (3√3 ÷ 2) × s²

≈ 2.598 × s². Square the side, multiply by 2.598.

Apothem

a = (√3 ÷ 2) × s

≈ 0.866 × s. Perpendicular from center to any side.

Perimeter

P = 6 × s

Six equal sides, each of length s.

From Apothem

s = (2 ÷ √3) × a

≈ 1.1547 × a. Also: R = s (circumradius equals side).

What Is a Regular Hexagon?

A regular hexagon is a six-sided polygon where all six sides are equal in length and all six interior angles are equal (each measuring 120°). It is one of only three regular polygons that can tile a flat plane without gaps — the others being the equilateral triangle and the square.

One remarkable property: a regular hexagon can be divided into exactly 6 equilateral triangles, all meeting at the center. This means the circumradius (center-to-vertex distance) equals the side length — a property unique to the regular hexagon among all regular polygons.

120°
Each interior angle of a regular hexagon
R = s
Circumradius equals side length
2.598 s²
Area in terms of side length

Worked Example

Regular hexagon with side 6 cm

Given: s = 6 cm
Area: A = (3√3/2) × 6² = (3√3/2) × 36 = 54√3 ≈ 93.53 cm²
Apothem: a = (√3/2) × 6 = 3√3 ≈ 5.196 cm
Circumradius: R = s = 6 cm
Perimeter:P = 6 × 6 = 36 cm

Common Hexagon Measurements

Side Apothem Area Perimeter
5 cm 4.33 cm 64.95 cm² 30 cm
6 cm 5.20 cm 93.53 cm² 36 cm
10 cm 8.66 cm 259.81 cm² 60 cm
15 m 12.99 m 584.57 m² 90 m
20 m 17.32 m 1039.23 m² 120 m

Real-World Applications

🐝

Nature — Honeycomb

Honeycomb cells are regular hexagons — the most efficient shape for packing the most area using the least wax.

⚙️

Engineering — Hardware

Hexagonal nuts, bolts, and wrench heads use the regular hexagon shape for optimal torque and grip.

🎮

Games — Hex Boards

Strategy games like Catan and many war games use hexagonal tile boards for equal movement in all directions.

🏗️

Construction — Tiling

Hexagonal floor tiles and paving patterns tile perfectly without gaps, providing both beauty and efficiency.

🔬

Science — Molecular Structure

The benzene molecule (C₆H₆) and graphene both exhibit regular hexagonal carbon ring structures, making hexagon area calculations relevant in chemistry and materials science.

Frequently Asked Questions

What is the formula for area of a regular hexagon?
The area of a regular hexagon is A = (3√3/2) × s² where s is the side length. This equals approximately 2.598 × s². For example, a hexagon with side 6 cm has area = 2.598 × 36 ≈ 93.53 cm².
Why does a regular hexagon have circumradius equal to side length?
A regular hexagon can be divided into 6 equilateral triangles all meeting at the center. In each equilateral triangle, the two sides connecting to the center (the circumradius) are equal to the base (one side of the hexagon). Therefore R = s — the circumradius equals the side length.
What is the apothem of a hexagon?
The apothem is the perpendicular distance from the center of the hexagon to the midpoint of any side (also called the inradius). For a regular hexagon: a = (√3/2) × s ≈ 0.866s. The area can also be calculated as A = (1/2) × perimeter × apothem.
How does a hexagon tile a plane perfectly?
Regular hexagons tile perfectly without gaps — only equilateral triangles, squares, and hexagons can do this among regular polygons. The 120° interior angles allow exactly 3 hexagons to meet at each vertex (3 × 120° = 360°), perfectly filling the plane with no overlap or gap.
How do you calculate area from the apothem?
From the apothem a, solve for side: s = 2a/√3. Then apply A = (3√3/2)s². Alternatively, use A = (1/2) × P × a = 3sa, where P = 6s is the perimeter. For a = 5.196 cm: s = 2 × 5.196/1.732 ≈ 6 cm → A ≈ 93.53 cm².

Related Area Calculators

Circle Semicircle Square Rectangle Parallelogram Rhombus Trapezium Scalene Triangle Right-Angle Triangle Equilateral Triangle Isosceles Triangle Sector & Segment