Spherical Cap Volume Calculator

Compute the volume, base circle radius, curved surface area, and total surface area of a spherical cap from the sphere radius and cap height.

Input

Enter the sphere radius and the cap height to compute the volume and surface area of a spherical cap at once.

Sphere radius R

Cap height h

Volume

113.097336

Base circle radius

4.582576

Curved surface area

94.24778

Total surface area

160.221225

Length keeps the input unit, area is squared, and volume is cubed.

A spherical cap is the dome shaped solid formed when a sphere is cut by a single plane.
The volume is V＝(πh²／3)×(3R−h), where R is the sphere radius and h is the cap height.
The radius of the flat base circle is a＝√(h×(2R−h)).
The curved (spherical) surface area is 2πRh, and adding the base circle area πa² gives the total surface area.
The height h must be no greater than the diameter 2R. When h equals 2R the cap becomes the whole sphere.
Length keeps the unit of the inputs, area is squared, and volume is cubed.

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