Maths & numbers
Spherical cap calculator
Calculate the volume, base radius and surface areas of a sphere cut by a plane.
A clear answer. Here’s how.
Requires cap height between zero and twice the sphere radius. Base radius = √[h(2R−h)], cap volume = πh²(R−h/3), curved area = 2πRh, and the closing disc area = πh(2R−h). At h=R this is a hemisphere; at h=2R it is a whole sphere. Uses one consistent length unit.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Sphere radius
- 5
- Cap height
- 2
Example result
- Cap volume
- 54.4542726622
- Base radius
- 4
- Curved surface area
- 62.8318530718
- Closing disc area
- 50.2654824574
- Closed total surface area
- 113.097335529