Hexagonal Prism Calculator
Calculate the volume, lateral surface area, and total surface area of a regular hexagonal prism.
Enter the side length and height to get results.
A regular hexagonal prism has two identical hexagonal bases connected by six rectangular faces. Every edge of both bases has the same length — call it a. The height h is the perpendicular distance between the two bases.
The base of a regular hexagon is made up of six equilateral triangles arranged around a center point. That gives the area formula: A = (3√3/2) × a², which comes out to roughly 2.598 × a². Double that for the two bases, multiply by height, and you have volume.
Volume = (3√3/2) × a² × h
The six rectangular sides are each a wide and h tall, so lateral surface area is simply 6ah. Total surface area adds the two bases:
Lateral SA = 6ah Total SA = 6ah + 3√3 × a²
A common mistake: the formula uses a squared, not a. If you double the side length, the base area — and therefore the volume — quadruples. Height stays linear.
Where you run into hexagonal prisms: structural steel columns with hexagonal cross-sections, hex bolts and nuts (which approximate this shape), honeycomb cells in beehives, pencils (classic hexagonal cross-section), and some packaging designs. The honeycomb pattern is particularly interesting because it maximizes enclosed area per unit of perimeter — which is why bees evolved it.
For very large or very small values, keep track of your units. Volume in cubic centimeters and surface area in square centimeters are two different things — mixing them up is the most common error when doing practical fabrication math.