Hexagonal Prism Volume Calculator
From a hexagon side and a length, get the volume, the cross-sectional area, and the surface area — the numbers that describe any regular hexagonal prism.
Two inputs, three answers
Enter the hexagon side and the prism length and the calculator returns the volume ((3√3/2)·s²·L), the cross-section area ((3√3/2)·s²), and the total surface area at once.
Keep units consistent
The side and length are unit-agnostic — your answers come back in the same unit (squared for the areas, cubed for the volume), so don't mix centimetres with inches.
What is a hexagonal prism volume calculator?
Side and length in, full prism out
A hexagonal prism volume calculator turns two measurements — the side length of a regular hexagon and the length of the prism — into the numbers that describe the whole solid: how much it holds (volume), the area of one hexagonal end face (cross-section area), and the area of its entire outside (surface area). A hexagonal prism is the shape of a pencil, a nut, a honeycomb cell, or a hex bolt: a regular six-sided face swept along a straight length. Because the cross-section is a regular hexagon, its area is fixed by the single side length, so those two inputs are all you need to describe the whole bar.
Enter the hexagon side and the prism length in any length unit to get the volume, cross-section area, and surface area instantly.
Three short formulas, all built from the side length s and the prism length L.
volume = (3√3 / 2) × s² × LA regular hexagon is six equilateral triangles arranged around a centre, so its area is (3√3/2) × s² — about 2.598 × s². The volume is that cross-section area multiplied by the prism length. The total surface area adds the two hexagonal end faces (2 × the cross-section) to the six identical rectangular sides (6 × s × L).
Suppose you have a hexagonal prism with a side of 4 and a length of 10.
Cross-section area
(3√3 / 2) × 4² = 2.598076 × 16 = 41.569219 square units — one hexagonal end face.
Volume
41.569219 × 10 = 415.692194 cubic units — the space inside.
Surface area
2 × 41.569219 + 6 × 4 × 10 = 83.138439 + 240 = 323.138439 square units — both ends plus the six sides.
The three outputs answer three different everyday questions. The volume (about 415.692194 cubic units for s = 4, L = 10) is how much the prism holds — the wax in a honeycomb cell, the metal in a hex bar, the water a hexagonal column would displace. The cross-section area (about 41.569219 square units) is the area of one end face; it is the figure that decides how strong a hexagonal beam is in bending, or how much material each slice of the bar contains, and it never changes along the length. The surface area (about 323.138439 square units) is the entire outside — both hexagonal ends plus the six rectangular sides — the figure you need to coat, plate, or wrap the prism. A useful sense-check: the cross-section area grows with the square of the side, so a side twice as long gives a face four times the area and a prism four times the volume at the same length.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Regular hexagons and consistent units
These formulas assume a regular hexagonal cross-section — all six sides equal and all angles 120° — swept straight along the length (a right prism). An irregular hexagon, a tapered or twisted bar, or a prism with rounded edges will differ from the computed value. The side and length are also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a side and length in centimetres give a volume in cubic centimetres and areas in square centimetres, never a mix.