What is the area of a regular hexagon?

The area of a regular hexagon with side length s is (3 times the square root of 3 divided by 2) times s squared, which is approximately 2.5981 times s squared. For example, a hexagon with side 6 has area approximately 2.5981 times 36 = 93.53 square units.

What are the two types of diagonal in a regular hexagon?

A regular hexagon has two distinct diagonal lengths. The long diagonal connects opposite vertices and equals twice the side length (2s). The short diagonal connects vertices separated by one vertex and equals s times the square root of 3, approximately 1.732 times s. For side length 6, the long diagonal is 12 and the short diagonal is approximately 10.39.

What is the apothem of a hexagon?

The apothem of a regular hexagon is the perpendicular distance from the centre to the midpoint of any side. It equals s times the square root of 3 divided by 2, approximately 0.866 times s. For side length 6 the apothem is approximately 5.20. The apothem is also the inradius and equals the circumradius times the cosine of 30 degrees.

Hexagon Calculator

A regular hexagon is a six-sided polygon where all sides are equal in length and all interior angles measure exactly 120 degrees. It is one of only three regular polygons that can tile a flat plane without gaps, which is why hexagonal shapes appear in beehives, carbon nanotubes, tile patterns, bolts and nuts, and engineering design. Because the hexagon has a high degree of symmetry, every property follows directly from a single measurement: the side length. You enter one value and the calculator returns everything else. The area is (3 times the square root of 3 divided by 2) times the side length squared. The perimeter is six times the side length. A regular hexagon has two distinct diagonal lengths. The long diagonal connects two opposite vertices and equals twice the side length. The short diagonal connects two vertices separated by one vertex and equals the side length times the square root of 3. The apothem is the perpendicular distance from the centre to the midpoint of any side and equals the side length times the square root of 3 divided by 2. The circumradius, which is the distance from the centre to any vertex, equals the side length exactly. This calculator is used in geometry coursework, engineering drawing, packaging design, tile layout, and material estimation. Results are in the same units as the side length.

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Side length (s)

93.53

area (square units)

Perimeter36.00

Long diagonal12.00

Short diagonal10.39

Apothem5.20

Circumradius6.00

How it works

For a regular hexagon with side length s: Area = (3 times sqrt(3) divided by 2) times s squared, approximately 2.5981 times s squared. Perimeter = 6 times s. Long diagonal = 2 times s (vertex to opposite vertex). Short diagonal = s times sqrt(3), approximately 1.7321 times s (vertex to vertex skipping one). Apothem = s times sqrt(3) divided by 2, approximately 0.8660 times s. Circumradius = s (the hexagon's circumradius always equals its side length).

Worked example

A regular hexagon with side length 6. Area = 2.5981 times 36 = 93.53 square units. Perimeter = 6 times 6 = 36.00. Long diagonal = 2 times 6 = 12.00. Short diagonal = 6 times 1.7321 = 10.39. Apothem = 6 times 0.8660 = 5.20. Circumradius = 6.00. These match the default values above.

Related calculators

Regular Polygon Calculator: calculate properties of any regular polygon from 3 to 12 sides.
Ellipse Calculator: area, circumference, and eccentricity for oval shapes.
Gear Ratio Calculator: apply hexagonal geometry to gear tooth counts.
Percent Error Calculator: verify measured dimensions against calculated values.

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