Rounded Cone Calculator

This function calculates various properties of a rounded cone. To perform the calculation, enter the radii of the base and the spherical cap and the height of the truncated cone. Then click on the 'Calculate' button.

Rounded Cone Calculator  Input Delete Entries Base radius R Cap radius r Trunc.cone height j Decimal places 0 1 2 3 4 6 8 10  Results Height of cap i Total height h Surface area S Volume V Cone base angle α

Formulas for rounded cones

Cone base angle (\(\small{α}\))

\(\displaystyle α = arccos\left( \frac{R - r}{\sqrt{ h^2 + ( R - r )^2}} \right) \)

Height of cap (\(\small{i}\))

\(\displaystyle i = \sqrt{\frac{ r^2 }{\frac{ 2 }{ 1 - cos(α) } - 1 }} \)

Surface area (\(\small{S}\))

\(\displaystyle S = (R + r) · π · \sqrt{(R - r)^2 + j^2} + π· R^2 + π · (r^2 + i^2) \)

Volume (\(\small{V}\))

\(\displaystyle V=\frac{π}{3} · j · \left( R^2 + R· r + r^2 \right) + i^2 * \left(\frac{ 3 · ( r^2 + i^2 ) }{ 2· i} - i \right) \)