Use one side length to find the key measurements of a regular six-sided hexagon.
A regular hexagon with side 4 has perimeter 24 and area 24√3 ≈ 41.569 square units. The formulas require all six sides to be equal.
Exact form: 24√3 square units.
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How to Use the Hexagon Calculator
Enter the length of any side of a regular hexagon and choose a length unit. The tool finds its area, perimeter, apothem, and center-to-vertex radius. It assumes six equal sides and equal interior angles; do not use these one-side formulas for an irregular hexagon.
Regular Hexagon Formulas
A regular hexagon splits into six equilateral triangles. Its perimeter is six side lengths. The apothem is the center-to-side perpendicular distance, while the vertex radius is the center-to-corner distance.
Worked Example: Side Length 4
The perimeter is 6 × 4 = 24 units. The apothem is (√3 ÷ 2) × 4 = 2√3 ≈ 3.464 units. Then area = ½ × 24 × 2√3 = 24√3 ≈ 41.569 square units. The radius from center to a vertex equals 4 units.
Why Six Equilateral Triangles Appear
Connecting the center to all six vertices makes six congruent triangles. Each has three equal sides: two radii and one edge of the hexagon. This geometry explains why the vertex radius equals the side and why the apothem uses the √3 factor.
Units and Irregular Hexagons
Perimeter, apothem, and radius use the entered length unit. Area uses the squared unit. For an irregular hexagon, one side length is not enough to determine area or perimeter; you would need additional sides, angles, coordinates, or a decomposition into known shapes.
Hexagon Calculator FAQs
What is the area of a regular hexagon with side 4?
24√3, about 41.569 square units.
What is its perimeter?
Six times the side length.
Can I use this for an irregular hexagon?
No. One side is insufficient for an irregular hexagon.
Editorial review
SolverCalc names Prof. Dr. Khalil Mudassar as its educational reviewer. The formulas and examples are documented in the references below.
Sources
Disclaimer
For educational use. Check your class or textbook convention when the problem defines a different range, sequence index, or notation.