Hexagonal Prism Volume Calculator

This hexagonal prism volume calculator works out the volume of a prism with a regular hexagonal cross section. Enter the hexagon side length and the length of the prism, choose your unit, and it returns the volume along with the base area. A prism has the same cross section all the way along, so its volume is simply the area of the base times the length. For a regular hexagon the base area is three times the square root of three, over two, times the side squared. The calculator handles that constant for you. It is unit agnostic, so metres give cubic metres and centimetres give cubic centimetres. Hexagonal prisms turn up as nuts and bolts, pencils, gazebo posts, honeycomb cells and packaging, so this is handy for engineering, woodworking and design as well as geometry study. The side length is the length of one edge of the hexagon, and the height is how long the prism is along its axis. The formula, a worked example and the assumptions are set out below so you can check the result.

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Base area 
Prism height10 m

The formula

The volume of a prism is the base area times the height. For a regular hexagon of side a the base area is (3 sqrt(3) / 2) a², so V = (3 sqrt(3) / 2) a² h, where h is the length of the prism. The constant 3 sqrt(3) / 2 is about 2.598076.

Worked example

A hexagonal prism with a side of 6 has a base area of (3 sqrt(3) / 2) times 36, about 93.53. Over a length of 10 the volume is about 935.31. Enter 6 and 10 above to confirm.

Frequently asked questions

What is the hexagonal prism volume formula?

V = the regular hexagon base area times the prism length. The base area is (3 times the square root of 3, over 2) times the side squared.

Does it assume a regular hexagon?

Yes. It assumes a regular hexagon with six equal sides. An irregular hexagonal cross section needs its base area worked out separately, then multiplied by the length.

What is the base area constant?

Three times the square root of three, divided by two, which is about 2.598076 times the side squared.

Who this calculator is for

This calculator is for students, engineers and woodworkers who need the volume of a regular hexagonal prism.

What this calculator assumes

  • The cross section is a regular hexagon with six equal sides.
  • You enter the hexagon side length and the prism length.
  • The volume is in the cube of your chosen unit.
  • Results are rounded for display.

Formula and sources

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