Primary Mathematical Formula
$$V = \frac{1}{12} n a^2 \cot(\pi/n) h$$
Frequently Asked Questions
How do you calculate the volume of a polygonal pyramid?
Calculate the polygon's base area, multiply it by the perpendicular height, and divide by 3.
What is the formula for a polygonal pyramid's volume?
The general formula is $V = \frac{1}{3} B h$. It applies to pyramids with triangular, square, pentagonal, hexagonal, heptagonal ($n=7$), octagonal ($n=8$), and higher polygonal bases.
How do I calculate the area of a regular polygon base?
Use $B = \frac{1}{2} P a$, where $P$ is the polygon's perimeter and $a$ is its apothem. For an $n$-sided polygon with edge length $s$, $B = \frac{n s^2}{4 \tan(\pi/n)}$.
Can a polygonal pyramid have an irregular base?
Yes. A polygonal pyramid can have a regular or irregular polygon as its base. For an irregular base, determine the surveyed base area before calculating volume.
Which measurements are required for a polygonal pyramid volume calculator?
You need the base area and perpendicular height, or the polygon's number of sides $n$, edge length $s$, and perpendicular vertical height $h$.