Volume of a spherical cap calculator
Enter the dimensions of a spherical cap and read off its volume and surface area. Volumes convert to litres and gallons with the unit selector.
Volume
54.454 273m³
- Surface area
- 62.831 853
- Base radius of the cap
- 4
- Share of the whole sphere
- 10.4000 %
Show the working
- Sphere radius = 5
- Cap height = 2
- Volume = pi * 2^2 * (3*5 - 2) / 3 = 54.4543
- Surface area = 2 * pi * 5 * 2 = 62.8319
- Base radius of the cap = 2 <= 2*5 ? sqrt(max(2*5*2 - 2^2, 0)) : 0 = 4
- Share of the whole sphere = 5 > 0 ? (2^2*(3*5-2)/3) / (4*5^3/3) * 100 : 0 = 10.4
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
The formula
- volume = pi h^2 (3r - h) / 3
- curved surface = 2 pi r h
This is the shape of liquid in the bottom of a spherical tank, and of the dome on a pressure vessel.
Switch the volume unit to litres or US gallons to read the capacity directly.