A spherical cap height is not its share of total volume.
Does a cap with one-quarter of sphere height hold one-quarter of its volume?
Use the matching calculator
Use this decision sequence
- Measure cap height from the sphere pole to the cutting plane.
- Check it lies between zero and the full sphere diameter.
- Use the cap formula with sphere radius, rather than a linear height fraction.
- Keep the curved cap surface and enclosed cap volume separately labelled.
Keep the quantities distinct
| Quantity or assumption | How to use it |
|---|---|
| Cap height | An axial distance from the pole. |
| Cap volume | Changes nonlinearly with height. |
| Hemisphere | The special case where cap height equals sphere radius. |
Worked comparison
For an illustrative sphere of radius 1 m, a 0.5 m-high cap occupies π×0.5²×(1−0.5/3) = 0.6545 m³. The full sphere holds 4.1888 m³, so the cap contains 15.625% of full volume although its height is 25% of the full diameter. At 1 m cap height, the volume becomes exactly one hemisphere.
Check before using the estimate
A spherical shape must actually fit the container; the model does not infer a real vessel’s profile.
All dimensions, product properties, prices and specifications in this example are illustrative arithmetic inputs. Use the values from your measured plan, selected product data sheet and supplier quote. This guide does not choose construction specifications or certify safety.
Calculation and scope checked 2026-10-04. Methods and scope.