Spherical Cap Calculation

This function calculates the volume and surface area of a spherical cap. A spherical cap or spherical dome is a portion of a sphere cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane.

To perform the calculation, enter the spherical radius and the height or radius of the cap. Then press the 'Calculate' button.

Formulas for calculating the cap of a sphere

Cap volume	\(\displaystyle V_s=\frac{1}{3}·π·h^2·(3·r - h)\)
Cap height	\(\displaystyle h=r-\sqrt{r^2 -a^2}\)
Cap radius	\(\displaystyle a= \sqrt{r^2-(r -h)^2}\)
Cap surface area	\(\displaystyle S=2·π·r·h\)
Cap base area	\(\displaystyle A=a^2 ·π\)
Total surface area	\(\displaystyle S_{Seg}=S+A\)
Radius	\(\displaystyle r=\frac{S}{2·π·h}\)