Polygon Prism Volume Calculator
Choose the number of sides, then enter the side length and height of a regular polygon prism for its volume and surface area, drawn to scale. Click a dimension on the drawing to change it.
Dimensions
Polygon PrismResult
Volume of a polygon prism
A polygon prism has two identical regular-polygon ends joined by rectangles, one per side. Its volume is the base polygon's area, n·a²⁄(4·tan(π⁄n)), times the height. The surface adds the two ends to the rectangular sides between them.
Editing on the drawing
Click the side length or the height on the figure, type a new value and press Enter to redraw the prism to scale. Change the number of sides in the panel to swap the base shape — triangle, pentagon, octagon and beyond.
How to find the volume of a polygon prism
A polygon prism has two identical regular-polygon ends connected by rectangles, one per side — a hexagonal nut, a pentagonal paver and an octagonal fence post are all polygon prisms, just with a different number of sides. Three measurements set a regular one: the number of sides, the side length, and the height of the prism.
The formulas
The volume is the base polygon's area times the height. A regular polygon of n sides and side length a has area n·a²⁄(4·tan(π⁄n)) — n identical isosceles triangles meeting at the centre. The surface adds the two polygonal ends to the n rectangular sides.
Worked example
Take a regular hexagonal (n = 6) prism with side 40 and height 84.
Area of a regular hexagon.
Base area times height.
Two ends plus six rectangles.
What else the calculator returns
You also get the base area, the lateral area, and the two radii that describe the base: the apothem (centre to the middle of a side) and the circumradius (centre to a vertex).
Where it comes up
Polygon-prism volumes describe bolts and nuts, pencils, paving and tiling, structural sections, fence posts and honeycomb — anything built from a regular cross-section swept along a length.
Frequently asked questions
How do you find the volume of a polygon prism?
Multiply the base polygon's area, n·a²⁄(4·tan(π⁄n)), by the height h, where n is the number of sides and a is the side length.
What is the area of a regular polygon?
For n sides of length a it is n·a²⁄(4·tan(π⁄n)) — n identical isosceles triangles meeting at the centre. This simplifies to (3√3⁄2)a² for a hexagon (n = 6).
What is the difference between the apothem and the circumradius?
The apothem is the distance from the centre to the middle of a side; the circumradius is the distance from the centre to a vertex. Spanner and bolt sizes typically quote twice the apothem, the "across flats" measurement.
How do I find the height from the volume?
Divide the volume by the base area: h = V ⁄ (n·a²⁄(4·tan(π⁄n))).
Does this assume a regular polygon?
Yes — all sides equal and all angles equal. An irregular polygon needs its own measured cross-section area.