Hexagonal Prism Surface Area Calculator

A regular hexagonal prism has two hexagon ends and six identical rectangular side faces.

SA = 2 × A_hexagon + 6 × (a × L) = 3√3 × a² + 6aL ≈ 5.196 × a² + 6aL

Where:

• a = hexagon edge length
• L = prism length
• A_hexagon = (3√3 / 2) × a²

Worked example — pencil lacquer coverage: A standard pencil with a = 3.7 mm, L = 175 mm. A_hexagon = 2.598 × 13.69 ≈ 35.57 mm². Two ends: 2 × 35.57 = 71.14 mm² (these are usually cut and left raw, or sealed with the eraser ferrule). Six side faces: 6 × 3.7 × 175 = 3,885 mm² = 38.85 cm² of lacquer area per pencil.

A pencil factory using powder coat or spray paint produces about 5-6 m² of lacquered surface per 100 pencils.

Worked example — honeycomb sandwich panel: A 600 × 1,200 mm aluminum honeycomb panel with cell edge 6 mm and panel thickness 25 mm. The cell count in a panel that size: Cell area = 2.598 × 36 = 93.5 mm² per hexagon. Panel area = 600 × 1,200 = 720,000 mm². Cells per panel ≈ 720,000 / 93.5 ≈ 7,700 cells.

Each cell has six interior walls (shared with neighbors, so count each cell’s wall surface as 3 walls × side area). Per cell: 3 × 6 × 25 = 450 mm² of interior wall. Total wall surface per panel: 7,700 × 450 ≈ 3.47 m² of aluminum foil in walls.

That’s how a panel weighing about 1 kg can carry many times its own weight — the hex cell geometry distributes loads across vast surface efficiently.

Where hexagonal prism surface matters:

• Pencil finishing. Lacquer, paint, brand stamping — all priced by surface area.
• Hex nut plating. Zinc, nickel, chrome — surface area drives plating cost.
• Honeycomb sandwich panels. Aerospace and racing-yacht construction.
• Hexagonal column wraps. Decorative architectural finishes.
• Crystallography display cases. Mineral specimens preserved in hex-prism vitrines.

Comparing to a cylinder of equivalent volume:

A hex prism with edge a is essentially a cylinder when a is small enough. For a hex prism with circumscribed-circle radius a (the corner-to-center distance), the equivalent cylinder has the same radius. Hexagon area = 2.598a², circle area = π × a² ≈ 3.142a². So a hexagon holds about 82.7% of its circumscribed circle’s area.

For the SAME outer “size” measured corner-to-corner, a cylinder holds about 21% more material than a hex prism, but with a smooth surface that’s harder to grip and roll.

The hex shape wins on grippability (for pencils and nuts) and tiling efficiency (for honeycomb structures), at the cost of slightly less volume.

Sanity check:

• L = 0: SA = 2 × hexagon area. ✓
• a = 0: SA = 0. ✓
• For a = 1, L = 1: SA = 5.196 + 6 = 11.196. ✓