Pyramid Volume Calculator
Determine the volume 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
heightis 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
nis 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:
- 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‰.
- 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).
- Determine the side length. The Cheops pyramid edge length is on average 230.36 m.
- 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||Edges||Vertices||Shape of base||Pyramid name|
Tetrahedron volume calculation
As an example, let's take the example of loose leaf tea pyramid:
- Choose the shape of the base. In our case, it's regular triangle.
- Type the pyramid's height. Assume that for a tea pyramid it's equal to 1.2 in.
- Enter the side length. For example, 1.5 in.
- 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.
The volume formula works for both right and oblique pyramids.