Octagonal Prism Volume Calculator
From an octagon side and a prism length, get the volume, the cross-section area, and the total surface area — the three numbers that describe any regular octagonal prism.
Two inputs, three answers
Enter the octagon side and the prism length and the calculator returns the volume, the cross-section area (one octagonal end), and the total surface area all at once.
Keep units consistent
The side and length are unit-agnostic — your answers come back in the same unit (squared for the area, cubed for the volume), so don't mix centimetres with inches.
What is an octagonal prism volume calculator?
Side and length in, full prism out
An octagonal prism volume calculator turns two measurements — the side length of a regular octagon and the length of the prism — into the numbers that describe a whole octagonal prism: how much it holds (volume), the area of one octagonal face (cross-section area), and the area of all its outer faces (surface area). A regular octagonal prism has two identical regular-octagon ends joined by eight equal rectangles, so once you know the side and the length every measurement is fixed. That makes those two inputs all you need for octagonal pencils, gazebo posts, nuts and bolts, prism-shaped containers, and any geometry homework where an octagonal prism shows up.
Enter the octagon 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, the prism length L, and a fixed octagon constant.
volume = 2(1 + √2) × s² × LThe cross-section area is the area of one regular octagon, 2(1 + √2) × s² — about 4.828427 × s². The volume is simply that area multiplied by the prism length L: a prism holds its cross-section stretched along its length. The total surface area is the two octagonal ends plus the eight rectangular sides, 2 × area + 8 × s × L.
Suppose you have a regular octagonal prism with a side of 4 and a length of 10.
Cross-section area
2(1 + √2) × 4² = 4.828427 × 16 = 77.254834 square units — one octagonal end.
Volume
77.254834 × 10 = 772.548340 cubic units — the space inside.
Surface area
2 × 77.254834 + 8 × 4 × 10 = 474.509668 square units — two ends plus eight rectangles.
The three outputs answer three different everyday questions. The volume (about 772.548340 cubic units for s = 4, L = 10) is how much the prism holds — the material in an octagonal bar, the capacity of a prism-shaped container. The cross-section area (about 77.254834 square units) is the size of one octagonal end, which is the same all the way along the prism; this is what you would see if you sliced straight through. The surface area (about 474.509668 square units) is the full outside skin — the two octagonal caps plus the eight rectangular sides — useful for wrapping, painting, or estimating material. A handy check: the volume always equals the cross-section area times the length, so doubling the prism length doubles the volume but leaves the cross-section unchanged. The octagon constant 2(1 + √2) ≈ 4.828427 is the thread tying it together — it links any octagon side to its area, and so to the whole prism.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Regular octagons and consistent units
These formulas describe a right prism with a regular octagonal cross-section — all eight sides equal and the two ends perpendicular to the length. An irregular octagon, an oblique prism (ends not square to the length), or 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 a surface area in square centimetres, never a mix.