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.
A regular hexagon is six equilateral triangles arranged around a centre point, which gives the area formula A = (3√3/2) × a², roughly 2.598 × a². Multiply that base area by the height and you have the volume. One base, not two.
Volume = (3√3/2) × a² × h
The doubling belongs to surface area, where both ends count. That is the mistake this shape invites, and a factor of two in the volume is not the kind of error you spot by eye.
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
Worked example: a hexagonal planter
A cedar planter with 30 cm sides, 45 cm tall. Base area = 2.598 × 900 = 2,338 cm². Volume = 2,338 × 45 = 105,215 cm³, which is 105 litres of potting soil. Compost is sold by the 50-litre bag, so that is three bags with a little left over. Lateral surface = 6 × 30 × 45 = 8,100 cm², the area you would be staining on the outside. Doubled for inside and out, 1.62 m².
Another mistake worth naming: the formula uses a squared, not a. Double the side length and the base area quadruples, so the volume does too. Height stays linear, which is why a planter twice as wide holds four times the soil while one twice as tall holds only twice.
Where you run into hexagonal prisms: structural steel columns with hexagonal cross-sections, hex bolts and nuts, honeycomb cells in beehives, pencils, and a fair amount of packaging. Of every shape that tiles a plane with no gaps, the hexagon encloses the most area for the least wall, which is the reason bees settled on it and the reason aerospace cores are built the same way.
Keep your units straight. Volume in cubic centimetres and surface area in square centimetres are different quantities, and confusing the two is the commonest error in practical fabrication maths.
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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