Spherical Cap Calculator

Calculate spherical cap volume and curved surface area.

Sphere Radius (R)Cap Height (h)

Enter radius and cap height above.

How to Use the Spherical Cap Calculator

Enter sphere radius and cap height to calculate spherical cap volume and surface-related values.

Practical Example

For sphere radius 5 and cap height 2, the cap volume is approximately 54.45 cubic units.

Factors That Affect the Result

Cap height must be measured perpendicular to the cutting plane and cannot exceed the sphere diameter.

Frequently Asked Questions

What is a spherical cap?

The portion of a sphere cut off by a plane.

Can cap height exceed the radius?

Yes, but it cannot exceed the full diameter.

What units are returned?

Volume uses cubic units and area uses squared units.

Related Tools

Understanding a Spherical Cap

A spherical cap is the portion of a sphere cut off by a plane. Its size can be described by the sphere radius and cap height, and the appropriate formula depends on whether you need cap volume or surface area.

Measure cap height along the central axis and use consistent units. A spherical cap is not automatically a hemisphere; that occurs only for a particular cut through the sphere. For real domes or vessels, wall thickness and non-spherical geometry can make practical capacity differ from the ideal result.

Understanding Spherical Cap Geometry

A spherical cap is the curved portion cut from a sphere by a plane. Its dimensions are commonly described with the sphere radius and cap height, and those values must satisfy the geometry of the original sphere. A cap height cannot be negative and should not exceed the sphere diameter.

Use consistent length units throughout the calculation. Volume results are cubic units and surface-area results are square units. For manufactured or measured parts, small errors in cap height can noticeably affect the result, so use reliable dimensions when precision matters.