Hexagon Area Calculator (Regular Hexagon)
Choose the measurement you know, enter a value, and calculate instantly.
Area from side (s): A = (3√3 / 2) × s²
Area from apothem (a): A = 2√3 × a²
Area from perimeter (P): A = (√3 / 24) × P²
How to Find the Area of a Hexagon
A hexagon is a six-sided polygon. In this calculator, we focus on a regular hexagon, where all six sides and all interior angles are equal. Regular hexagons show up everywhere: floor tiles, nuts and bolts, beehive structures, landscape design, and game maps.
If you can measure one key value—side length, apothem, or perimeter—you can quickly compute the area. This page gives you both an instant calculator and the formulas so you can check the math yourself.
Key Measurements You Can Use
1) Side Length (s)
The side length is the distance of one outer edge. For a regular hexagon, all sides are equal, so measuring one side is enough.
2) Apothem (a)
The apothem is the distance from the center of the hexagon straight out to the midpoint of any side. It is not the same as radius. In many practical layouts, the apothem is easy to measure from centerline drawings.
3) Perimeter (P)
The perimeter is the total length around the shape. For a regular hexagon, P = 6s. If you already have perimeter, area can be found directly without first solving for side length.
Area Formulas for a Regular Hexagon
- From side length: A = (3√3 / 2) × s²
- From apothem: A = 2√3 × a²
- From perimeter: A = (√3 / 24) × P²
All three equations are equivalent for a regular hexagon. Use whichever matches your available measurement.
Worked Example
Suppose side length s = 10 cm. Then:
A = (3√3 / 2) × 10² = (3√3 / 2) × 100 = 150√3 ≈ 259.81 cm²
So the area is approximately 259.81 square centimeters.
Common Mistakes to Avoid
- Using formulas for an irregular hexagon with regular hexagon measurements.
- Mixing units (for example, side in meters and apothem in centimeters).
- Forgetting that area units are squared (cm², m², ft², etc.).
- Confusing radius, apothem, and diagonal length.
When the Hexagon Is Not Regular
If your hexagon has unequal sides or angles, the formulas above do not apply directly. In that case, split the shape into triangles, use coordinate geometry, or apply CAD tools. This calculator is intentionally optimized for the regular case because it is the most common in design and engineering tasks.
Quick Practical Uses
- Estimating tile coverage for hexagonal floor patterns
- Planning material for hexagonal tabletops and garden pavers
- Calculating painted surface regions in fabrication projects
- Checking dimensions in drafting, architecture, and STEM assignments
Final Tip
For best accuracy, measure once carefully and keep your units consistent from start to finish. Then use this calculator to instantly get area plus related dimensions (side, perimeter, and apothem).