Spherical Cap Volume Calculator

About this calculator

A spherical cap is the portion of a sphere cut off by a single plane, and this calculator finds its volume, V = (π·h²/3)·(3R−h), and curved surface area, 2·π·R·h, from the parent sphere's radius R and the cap's height h (measured from the cutting plane to the top of the cap). The formulas come from integrating circular cross-sections along the cap's axis.

Engineers use spherical-cap geometry to design dome roofs, tank heads (the rounded ends of pressure vessels), and lens surfaces, since a dome or a convex tank end is exactly a cap shape. Astronomers use the same geometry to describe the visible illuminated portion of a moon or planet, and manufacturers of domed containers, contact lenses, and architectural domes rely on this calculation during design. Engineering students and architects sizing a domed structure use this calculator to get exact volume and surface figures rather than approximations.