This all-in-one online Pyramid Volume Calculator performs calculations using the volume formula for an arbitrary pyramid, which relates the pyramid volume to the height of the pyramid and the area of its base. In case of a pyramid with regular base the base side is used for calculation instead of the area. Choose the type of the pyramid base, then enter the values of any two known parameters in the fields of this calculator and find the missing one.
Pyramid Volume Formula
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point lying outside the plane of the base, called the apex.
A right pyramid has its apex directly above the centroid of its base. A non-right pyramid is called oblique pyramid. A regular pyramid has a regular polygon base and is usually implied to be a right pyramid.
For a general pyramid the formula for the volume \(V\) is as follows:
$${\displaystyle V={\frac {1}{3}} \cdot A \cdot h},$$
where \(h\) is the height of the pyramid from the base to the apex, \(A\) is the area of its base.
This formula is valid for any polygon, regular or irregular, and any apex position, provided that \(h\) is measured as the perpendicular distance from the plane containing the base to the apex.
The volume of a pyramid whose base is a regular polygon is expressed by the following formula:
$${\displaystyle V={\frac {n}{12}} \cdot a^{2} \cdot h \cdot cot \left (\frac {\pi}{n} \right )},$$
where \(n\) is the number of the sides of the base, \(a\) is the length of the side.
Note that we do not specify units of measurement in our Pyramid Volume Calculator. We assume that the height and base side are measured in the same units of length, the base area is measured in square units of length, and volume is measured in cubic units of length (e.g., m, m2 and m3).
Related calculators
Check out our other geometry calculators such as Cylinder Volume Calculator or Cone Volume Calculator.