Math
Sphere volume and surface area
Find the surface area and volume of a sphere.
Calculators / Math / Spherical cap
Spherical cap calculator
Measure a cap cut from a sphere using the sphere radius and cap height.
On this page
Cap volume54.45units³
Curved surface area62.83units²
Base radius4units
Calculator controls
How to calculate
Measure a cap cut from a sphere using the sphere radius and cap height.
Cap volume =
pi*h^2*(3*R-h)/3 units³Curved surface area =
2*pi*R*h units²Base radius =
sqrt(h*(2*R-h)) unitsWorked example
- Sphere radius: 5
- Cap height: 2
- Cap volume: 54.45 units³
- Curved surface area: 62.83 units²
- Base radius: 4 units
Assumptions and limits
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded. Cap height must lie between zero and twice the sphere radius. Surface area excludes the flat base.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Measure a cap cut from a sphere using the sphere radius and cap height. Measure height from the cutting plane to the top of the cap, not from the sphere centre.
When this tool is useful
Measure height from the cutting plane to the top of the cap, not from the sphere centre.
Understanding your inputs
| Input | Example |
|---|---|
Sphere radius R | 5 |
Cap height h | 2 |
Frequently asked questions
Which assumptions matter for this result?
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded. Cap height must lie between zero and twice the sphere radius. Surface area excludes the flat base.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.