Hexagonal Prism Volume Calculator
A hexagonal prism is a three-dimensional solid whose two parallel bases are regular hexagons and whose six lateral faces are rectangles. It appears throughout engineering and nature — from honeycomb cells and hexagonal bolts to architectural columns and pencil shafts. This calculator instantly computes the volume, base area, lateral surface area, and total surface area of any regular hexagonal prism from just two measurements: the base edge length and the height.
The Volume Formula
The volume of a regular hexagonal prism is derived by multiplying the area of the hexagonal base by the height of the prism:
V = (3√3 / 2) × a² × h
where a is the edge length of one side of the regular hexagonal base and h is the perpendicular distance between the two bases (the prism height). The constant 3√3 / 2 ≈ 2.5981 is the coefficient that relates the side length squared to the area of a regular hexagon.
For example, a hexagonal prism with a = 5 cm and h = 10 cm has a base area of approximately 64.95 cm² and a volume of approximately 649.52 cm³.
Surface Area Formulas
In addition to volume, this tool also computes both surface area measurements:
- Lateral Surface Area — the combined area of the six rectangular side faces:
LSA = 6 × a × h - Total Surface Area — the complete outer surface including both hexagonal ends:
TSA = LSA + 2 × (3√3 / 2) × a²
Use lateral surface area when calculating material needed for the sides only (such as wrapping or painting). Use total surface area when calculating the complete enclosing material (such as sheet metal for a tank or coating for a structural column).
Supported Units
The calculator supports six common length units: millimetres (mm), centimetres (cm), metres (m), inches (in), feet (ft), and yards (yd). Both inputs — edge length and height — use the same selected unit. Volume results are shown in the unit cubed (e.g. cm³) and surface areas in the unit squared (e.g. cm²).
Practical Applications
Hexagonal prisms arise in a wide range of practical contexts:
- Engineering and manufacturing — calculating material volume for hex bar stock, hex bolts, and nuts used in mechanical assemblies
- Architecture and construction — estimating concrete or fill volume for hexagonal columns, pillars, and structural members
- Biology and materials science — modelling honeycomb cells, basalt column formations, and carbon nanotube cross-sections
- Packaging and storage — computing the volume of hexagonal containers, candles, and decorative packaging
How to Use This Calculator
Enter the base edge length — the length of any one side of the hexagonal base — and the height of the prism. Select your preferred unit from the dropdown. Results update instantly as you type. Use the decimal places control to adjust precision, and click Show Step-by-Step to expand the full derivation showing exactly how each value was calculated. The Copy All button copies all results and steps to your clipboard.
Tips for Accurate Measurement
For physical objects such as hex bar stock or nuts, measure the flat-to-flat distance (also called the wrench size) rather than the edge length. To convert: a = (flat-to-flat distance) / √3. This is important because most hex bars are sold by their flat-to-flat dimension, not the actual edge length. The edge length is the distance between adjacent corner vertices of the hexagon.