How it works
Use the radius of the whole sphere, not the radius of the cut base circle. Height h runs from the cutting plane to the cap’s outer tip and must be between 0 and 2R. With R = 1 and h = 1 the cap is a hemisphere, with volume 2π/3. The curved area excludes the flat base.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Full sphere radius | 5 | Enter a numeric value. Distance from the centre to the edge; half the diameter. Must be greater than zero. |
| Cap height from cutting plane to tip | 2 | Enter a numeric value. Use a non-negative value. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Full sphere radius
- 5
- Cap height from cutting plane to tip
- 2
Complete example results
- Cap volume
- 54.45427266
- Curved surface area
- 62.83185307
- Base radius
- 4
Reading the result
Enter lengths in the same unit. Area uses the square of that unit and volume its cube. Height is perpendicular to the base; use a sloping side only when the input explicitly asks for it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
Does a cap higher than the radius remain valid?
Yes. For R < h ≤ 2R the cap contains more than half the sphere. At h = 2R it becomes the full sphere and the base circle shrinks to radius zero.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: mathworld.wolfram.com