Primary Mathematical Formula
Frequently Asked Questions
How does the base shape affect a pyramid's volume?
The base shape determines how you calculate the base area $B$. Once the base area is known, every pyramid uses the exact same volume formula: $V = \frac{1}{3} B h$.
How do you calculate the volume of a square-base pyramid?
Square the base side length ($B = s^2$), multiply by the perpendicular height $h$, and divide by 3: $V = \frac{1}{3} s^2 h$.
How do you calculate the volume of a rectangular-base pyramid?
Multiply the base length $l$ by width $w$ ($B = l w$), multiply by perpendicular height $h$, and divide by 3: $V = \frac{1}{3} l w h$.
Can I calculate the volume of a pentagonal or hexagonal pyramid?
Yes. Calculate the regular pentagon area ($B = \frac{5}{4} s^2 \cot(36^\circ)$) or hexagon area ($B = \frac{3\sqrt{3}}{2} s^2$), multiply by perpendicular height $h$, and divide by 3.
What if my pyramid has an irregular polygon base?
Divide the irregular polygon into simpler triangles or rectangles, calculate and sum their areas to find $B$, then apply $V = \frac{1}{3} B h$.
Do all pyramid shapes use the same volume formula?
Yes. The formula $V = \frac{1}{3} B h$ applies universally to all pyramids regardless of base polygon shape, provided $B$ is the true base area and $h$ is the perpendicular vertical height.
Which pyramid calculator should I use?
Choose the calculator that matches your base geometry and known dimensions: use the Square or Rectangular pyramid calculator when those base dimensions are known, the Frustum calculator for truncated solids, or the General pyramid calculator when you already have the base area.