Hexagonal Prism Calculator

What is a Hexagonal Prism?

A hexagonal prism is a three-dimensional geometric shape with a regular hexagonal cross-section extruded along a straight length. It has eight faces: two hexagonal end caps (bases) and six rectangular lateral faces. A regular hexagonal prism has a regular hexagon (all six edges equal, all angles 120 degrees) as its cross-section. Hexagonal prisms are common in mechanical engineering, architecture, and nature. Use our Hexagon Calculator for the base shape and Rectangular Prism Calculator for similar 3D calculations.

The most familiar example of a hexagonal prism is a standard pencil — the hexagonal shape prevents it from rolling off a desk and provides three comfortable finger-gripping positions. Other common examples include nuts and bolt heads, hex bar stock used in machining, and honeycomb cells built by bees.

Formulas and Calculations

For a regular hexagonal prism with hexagon edge (a) and prism length (L):

Cross-Sectional Area (Ahex): Ahex = (3√3 / 2) × a²

The hexagonal area is computed by dividing the hexagon into six equilateral triangles of side length a.

Volume (V): V = Ahex × L = (3√3 / 2) × a² × L

The volume is the cross-sectional area multiplied by the prism length.

Total Surface Area (S): S = 3√3 × a² + 6 × a × L

The total surface area includes both hexagonal end caps plus all six rectangular lateral faces.

Lateral Surface Area (Slat): Slat = 6 × a × L

The lateral area covers only the six rectangular sides (no caps).

How to Use the Hexagonal Prism Calculator

Enter the hexagon edge length (a) and the prism length (L). The calculator instantly computes the volume, total surface area, lateral surface area, and hexagon cross-sectional area. All calculations are performed entirely in your browser with no server requests.

Frequently Asked Questions

How do you calculate the volume of a hexagonal prism?

Multiply the hexagonal cross-section area by the prism length: V = (3√3 / 2) × a² × L. For a hex bar with edge a = 2 m and length L = 5 m: V = (3√3/2) × 4 × 5 = 30√3 ≈ 51.96 m³.

What is the difference between lateral and total surface area?

Lateral surface area (Slat = 6aL) counts only the six rectangular side faces — useful when the ends are open or not being coated. Total surface area (S = 3√3 a² + 6aL) adds the two hexagonal end caps — use this when you need to paint, wrap, or plate the entire solid.

Where are hexagonal prisms used in real life?

Most nuts and bolt heads are hexagonal prisms — the six flats let a wrench grip from any of three angles. Pencils are hexagonal so they don't roll. Bees build honeycomb out of hexagonal-prism wax cells because the shape tiles the plane with the least wall material. Hex bar stock is a standard machinist input for parts needing anti-rotation grip.

How many faces, edges, and vertices does a hexagonal prism have?

A hexagonal prism has 8 faces (2 hexagonal caps + 6 rectangular lateral faces), 18 edges (6 on each cap + 6 lateral), and 12 vertices (6 on each cap). Euler's formula confirms it: V - E + F = 12 - 18 + 8 = 2.

What is the apothem of a hexagonal prism?

The apothem is the perpendicular distance from the center of the hexagonal cross-section to the midpoint of an edge: apothem = a × √3 / 2 ≈ 0.866a. It equals half the flat-to-flat distance across the hexagon, which is the dimension that wrench sizes are based on.

What is the circumradius of a regular hexagon?

For a regular hexagon, the circumradius (center-to-vertex distance) equals the edge length: R = a. This is a unique property of hexagons among regular polygons, because a regular hexagon decomposes into six equilateral triangles, all of which have side length a.

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What is a Hexagonal Prism?

Formulas and Calculations

How to Use the Hexagonal Prism Calculator

Frequently Asked Questions

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