Hexagonal Prism Volume Calculator

Volume of a regular hexagonal prism

A regular hexagonal prism has two parallel regular-hexagon bases of side L joined by rectangular side faces of height h. The base area is A = (3√3/2)·L², so the volume is V = A·h = (3√3/2)·L²·h ≈ 2.598·L²·h. Example: with L = 2 cm and h = 10 cm, V ≈ 2.598 · 4 · 10 ≈ 103.9 cm³. The hexagon is the polygon that tiles the plane with the smallest perimeter per unit area (Hales, 1999) — that is why honeycomb structures are optimal.

Applications

Hexagonal prisms appear in quartz crystals, which naturally grow as elongated hexagonal prisms with pyramidal caps; in graphite and graphene layers, where carbon atoms sit on a hexagonal lattice; in honeycomb sandwich panels used in aerospace to combine light weight with stiffness; in hex tiles (floors, façades, board games); and in hexagonal pencils, whose flat sides make them easier to grip and stop them from rolling off desks.

FAQ

Why the factor 3√3/2? A regular hexagon decomposes into six equilateral triangles of side L; each has area (√3/4)·L², so the total is 6·(√3/4)·L² = (3√3/2)·L².

What if the hexagon is irregular? The formula assumes a regular hexagon. For an irregular one, compute the base area directly (e.g. with the shoelace formula) and multiply by h.

What about an oblique hexagonal prism? Use the perpendicular height between the bases, not the slant edge — Cavalieri's principle guarantees the volume is the same as the right prism with that height.