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Spherical-Cap Surface Area from Radius and Cap Height Calculator

S_cap = 2 · π · R · h (curved part); S_total = 2·π·R·h + π·a².

Compute the curved (spherical) surface area S_cap = 2·π·R·h of a spherical cap of height h cut from a sphere of radius R, plus the planar circular base π·a² where a = √(2·R·h − h²). Total surface includes both. Used in domed structures, contact-lens optics, and meteorology (cap-cloud area).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

S_cap = 2 · π · R · h; a² = 2·R·h − h²; total = S_cap + π·a².

In depth

Compute the curved (spherical) surface area S_cap = 2·π·R·h of a spherical cap of height h cut from a sphere of radius R, plus the planar circular base π·a² where a = √(2·R·h − h²). Total surface includes both. Used in domed structures, contact-lens optics, and meteorology (cap-cloud area).