Spherical cap volume calculator
A spherical cap is the piece of a sphere cut off by a plane, like a shallow dome or liquid at the bottom of a round vessel.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter sphere radius, cap height and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Volume = πh²(3r − h)/3, base radius = √(h(2r − h)), curved area = 2πrh.
Example
Inputs: Sphere radius = 5, Cap height = 2, Length unit = Centimeter (cm). Result: Volume: 54.4543 cm³; Base radius: 4 cm; Curved surface area: 62.8319 cm².
Limits and caveats
- Assumes the cap is part of a true sphere; pointed architectural domes do not fit.
- Results are in the cube or square of the unit you chose, so enter every dimension in that same unit.
Questions about this tool
What is the spherical cap volume formula?
Volume = πh²(3r − h)/3. A sphere of radius 5 with a cap 2 high gives 52π/3, about 54.45.
What if the height equals the radius?
The cap is a hemisphere and the formula gives 2/3 × π × r³.
How do I find the sphere radius from the cap base?
Use r = (a² + h²) / (2h), where a is the base radius and h the cap height.