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Hexagon Calculator

Calculate regular hexagon area, perimeter, apothem, long diagonal, short diagonal, and circumradius with step-by-step steps.

Regular Hexagon Geometry
Area
93.5307
Perimeter
36
Long Diagonal (2s)
12
Short Diagonal (s√3)
10.3923
Deduction Steps:
Regular polygon with n = 6 sides, side length s = 6
Perimeter: P = n × s = 6 × 6 = 36
Interior Angle: ((n - 2) × 180°) / n = ((6 - 2) × 180) / 6 = 120°
Exterior Angle: 360° / n = 360 / 6 = 60°
Apothem (inradius): a = s / (2 · tan(π/n)) = 5.1962
Circumradius: R = s / (2 · sin(π/n)) = 6
Area: A = ½ × P × a = 0.5 × 36 × 5.1962 = 93.5307
Long diagonal (d_long): 2s = 12
Short diagonal (d_short): s√3 = 10.3923
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What Is a Hexagon Calculator?

A regular hexagon is a six-sided polygon with six equal sides and six equal interior angles of 120°. It is composed of six congruent equilateral triangles meeting at the center.

How to Use This Calculator

  1. Enter the side length (s) of the regular hexagon.
  2. View the calculated Area, Perimeter, Long Diagonal, Short Diagonal, and Apothem.
  3. Review the step-by-step geometric derivations.

Regular Hexagon Geometric Formulas

A = \frac{3\sqrt{3}}{2}s^2 \approx 2.59808s^2, \quad P = 6s, \quad d_{\text{long}} = 2s, \quad d_{\text{short}} = s\sqrt{3}

Because a regular hexagon consists of 6 equilateral triangles of area (√3/4)s², total area is 6 × (√3/4)s² = (3√3/2)s².

Worked Example

Scenario: Find area and diagonals for a regular hexagon with side s = 8 cm

Perimeter: P = 6 × 8 = 48 cm

Area: A = (3√3 / 2) × 8² = (3√3 / 2) × 64 = 96√3 ≈ 166.2769 cm²

Long diagonal: d_long = 2 × 8 = 16 cm

Short diagonal: d_short = 8√3 ≈ 13.8564 cm

Result: Area ≈ 166.28 cm², Perimeter = 48 cm, Diagonals: 16 cm & 13.86 cm

Tips & Key Notes

  • The circumradius (radius of circle passing through vertices) equals the side length: R = s.
  • The apothem (inradius) is (s√3) / 2 ≈ 0.866025 × s.
  • Hexagons tessellate perfectly without gaps, which is why honeybees build hexagonal honeycombs.

Frequently Asked Questions

Why do regular hexagons tile the plane?

Each interior angle is 120°. Three hexagons meet at a vertex: 120° × 3 = 360°, leaving no gaps and no overlap.

What is the long diagonal vs short diagonal?

The long diagonal connects opposite vertices through the center (d = 2s). The short diagonal connects vertices separated by one corner (d = s√3).

What is the sum of interior angles in a hexagon?

The sum is (6 - 2) × 180° = 720°. Divided by 6, each angle is 120°.

How do you find the area from the perimeter?

First divide perimeter by 6 to find side s, then apply A = (3√3/2)s².

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