Pyramids with regular base
Shape of base
Select...
Height
in
Side length
in
Volume
cu in
Base area known
Base area
in²
Height
in
Volume
cu in

Determine the area of any pyramid-like solid with our pyramid volume calculator. Choose between two options: calculate the volume of a pyramid with a regular base, so you need to have only side, shape and height given, or directly enter the base area and the pyramid height. The calculator doesn't have any problems with determining tetrahedron volume or volume of a square pyramid. If you are still not sure how to use the tool and how to calculate the pyramid volume - keep reading!

Pyramid volume formula

A pyramid is a polyhedron formed by connecting a polygonal base and an apex. The basic formula for pyramid volume is the same as for a cone:

  • volume = (1/3) * base_area * height, where height is the height from the base to the apex.

That formula is working for any type of base polygon and oblique and right pyramids. All you need to know are those two values - base area and height. However, there are other useful formulas, in case you don't know the base area. For any pyramid with a regular base, you can use the equation:

  • volume = (n/12) * height * side_length² * cot(π/n), where n is number of sides of the base for regular polygon

How to calculate the pyramid volume? Volume of a square pyramid calculation example

We know the formula, and what's next? How to use this pyramid volume calculator? The best choice to demonstrate how it works is the world's best-known pyramid - Cheops pyramid:

  1. Select the base shape. For Cheops pyramid, also called the pyramid of Khufu, it's a square. Of course, it's not an ideal square, but we can assume it is - the difference between the length of the edges is smaller than 1‰.
  2. Enter the height of a pyramid. Khufu pyramid height is equal to 146 m (you can change the units to meters with a simple click on the unit. Also you can check out our volume converter).
  3. Determine the side length. The Cheops pyramid edge length is on average 230.36 m.
  4. The approximate volume of a square pyramid is equal to 2,582,532 m³.

Pyramid volume names

A pyramid with an n-sided base has:

  • n+1 faces (n-triangles + 1 n-gon)
  • 2n edges
  • n+1 vertices

Name of the pyramid comes from the shape of the base:

Faces EdgesVerticesShape of basePyramid name
464 triangle tetrahedron/triangular pyramid
585 squaresquare pyramid
6106 pentagonpentagonal pyramid
7127 hexagonhexagonal pyramid
8148 heptagonheptagonal pyramid
9169 octagonoctagonal pyramid

Tetrahedron volume calculation

As an example, let's take the example of loose leaf tea pyramid:

  1. Choose the shape of the base. In our case, it's regular triangle.
  2. Type the pyramid's height. Assume that for a tea pyramid it's equal to 1.2 in.
  3. Enter the side length. For example, 1.5 in.
  4. Tetrahedron volume appears below. For our tea pyramid, it is equal to 0.39 cu in.

If you want to calculate the regular tetrahedron volume- the one in which all four faces are equilateral triangles, not only the base - you can use the formula:

volume = a³ / 6√2, where a is the edge of the solid

The height, in this case, can be calculated as: height = a√3 / 6 ~ 0.2887 * a, so if you want to calculate, e.g. the volume of a regular polyhedron with the edge = 3, type 3 * 0.2887 into the pyramid volume calculator "Height" box.

What next?

Now you are an expert and you know exactly how to calculate the pyramid volume! Why not to check the other volume calculators?

Hanna Pamuła, PhD student

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