🛑 Hexagon Calculator
Calculate the area, perimeter, side length, and radii of a regular hexagon.
Formulas (Regular Hexagon)
- Area = (3√3 / 2) × a²
- Perimeter = 6a
- Inradius (apothem) = (√3 / 2) × a
- Long Diagonal = 2a
- Short Diagonal = √3 × a
The Comprehensive Guide to Hexagon Calculator
What is a Hexagon Calculator?
A Hexagon Calculator is a specialized geometry tool used to find all the key metric properties of a regular hexagon instantly.
By entering just a single known measurement—like the side length, area, perimeter, inradius (apothem), or circumradius—the calculator automatically computes every other geometric property of the six-sided shape. It's built specifically for regular hexagons, where all six sides and all six interior angles are perfectly equal to one another.
The Mathematical Formula
Where s is the length of one side of a regular hexagon.
Calculation Example
Let’s calculate the properties of a regular hexagon with a Side Length (a) of 5 cm:
- 1. Perimeter: 6 × 5 = 30 cm
- 2. Area: (3√3 / 2) × 5² ≈ 64.9519 cm²
- 3. Inradius (Apothem): (√3 / 2) × 5 ≈ 4.3301 cm
- 4. Circumradius: Equal to a = 5 cm
Strategic Use Cases
- Architecture & Tiling: Hexagrams tessellate perfectly (they interlock without gaps), making them ideal for floor tiling, honeycomb structures, and patio layouts.
- Manufacturing: Calculating the exact cross-sectional area and wrench clearances required for hexagonal nuts and bolts.
- Tabletop Gaming: Designing hex-grid maps for strategy games where exact cell area and distance between hex centers (the Apothem) must be known.
Frequently Asked Questions
What is the difference between a long diagonal and short diagonal?
A regular hexagon has two types of diagonals. The Long Diagonal (D) connects opposite vertices and passes straight through the center (length = 2a). The Short Diagonal (d) connects two non-adjacent vertices, bypassing the center entirely (length = √3 × a).
What is an Apothem?
The apothem is the geometric term for the 'Inradius'. It is the perpendicular distance starting from the exact center of the hexagon and ending at the midpoint of any of its six flat sides. It is crucial for calculating the area.
How accurate is this calculator?
Our calculator uses industry-standard formulas to provide the most accurate results possible. However, it should be used for informational purposes only and not as a basis for formal calculations or legal advice.