Frustum Pyramid Calculator

This function calculates various parameters of a frustum pyramid. The frustum pyramid consists of a regular frustum or truncated pyramid and a pyramid placed on the larger base.

To calculate, enter the side lengths a and b, the heights of the pyramid and the frustum (truncated pyramid) and the number of corners. Then click on the 'Calculate' button.

Frustum pyramid calculator   Input Delete Entries Side length a Side length b Pyramid height j Frustum height i Number vertices n Decimal places 0 1 2 3 4 6   Results Overall height Base area Surface pyramid Later. surface frustum Entire surface Volume pyramid Volume Frustum Total volume Base perimeter

Formulas for the frustum pyramid

Overall height

\(\displaystyle h=i+j \)

Perimeter of the base

\(\displaystyle P =b*n\)

Base surface

\(\displaystyle A = \frac{ n · a^2 }{ 4 · tan(\frac{π}{n})} \)

Lateral surface frustum

\(\displaystyle L_F = \frac{n}{4} · (a + b) * \sqrt{cot^2\left(\frac{π}{n}\right) · (a - b)^2 + 4· i^2 } \)

Lateral surface pyramid

\(\displaystyle L_P = n · b · \frac{\sqrt{j^2 + \frac{1}{4} · b^2 · cot^2(\frac{π}{n})}}{2} \)

Entire surface

\(\displaystyle S = A+ L_F+L_P \)

Volume frustum

\(\displaystyle V_F = \frac{i}{3} · \left(\frac{n · (a^2 + b^2)}{4 · tan(\frac{π}{n})} + \sqrt{\frac{ n^2 · a^2 · b^2 }{ (4 · tan(\frac{π}{n}))^2}} \right) \)

Volume pyramid

\(\displaystyle V_P = \frac{n · b^2 · j}{12 · tan(\frac{π}{n})} \)

Volume

\(\displaystyle V = V_F+V_P \)