When to use this calculator
Find the volume cut from a sphere by a plane at a chosen cap height. Cap height ranges from zero to the full sphere diameter.
Explore the volume & surface area calculators for other questions in this topic. For a related calculation, use the Torus Surface Area Calculator: Find the outside surface area of a ring-shaped torus.
PUTTING IT INTO PRACTICE
Spherical Cap Volume: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Sphere radius | 5 |
| Cap height | 2 |
| Result | 54.454273 cubic units |
- Check the input labels and enter the example values above.
- Apply the relationship: Cap volume = πh²(3r−h)/3.
- The result is 54.454273 cubic units, rounded for display.
How to interpret your result
Cap height ranges from zero to the full sphere diameter.
Volume and surface area have different units and answer different questions. Use internal dimensions for capacity. A closed-solid surface area includes bases and lids unless the calculator explicitly describes an open shape.
Frequently asked questions
Should I use internal or outside measurements?
Use internal measurements for capacity and outside measurements for covering the exterior. Match the formula to the part being measured.
When is the spherical cap volume calculator useful?
Find the volume cut from a sphere by a plane at a chosen cap height. Cap height ranges from zero to the full sphere diameter.
How do I use the spherical cap volume calculator?
Enter sphere radius, cap height. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Cap volume = πh²(3r−h)/3.
What should I check before using the result?
Cap height ranges from zero to the full sphere diameter.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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