How does the Spherical Cap Calculator work?

Volume = (πh²/3) × (3r - h) where h = cap height, r = sphere radius Then: Surface area (curved) = 2πrh Then: Full sphere cap (h = 2r) gives 4πr² (full sphere surface) Then: Constraint: 0 < h ≤ 2r.

Can you give an example of how to use the Spherical Cap Calculator?

Example: Input r=10, h=3 gives a result of Vol 282.7.

Is the Spherical Cap Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Spherical Cap Calculator?

Our Spherical Cap Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

What formulas does this Spherical Cap Calculator use?

This calculator uses standard chemistry formulas as taught in A-Level, AP, and university courses. Results are rounded to appropriate significant figures.

Mathematics

Spherical Cap Calculator

Spherical Cap

Sphere radius (r)

Cap height (h)

Calculates spherical cap volume and surface area from sphere radius and cap height.

Symbol	Name	Unit	Description
h	2r) gives 4πr² (full sphere surface)	—	2r) gives 4πr² (full sphere surface)
r	sphere radius	—	sphere radius

Difficulty:intermediate

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Did You Know?

Earth's polar ice caps are spherical cap approximations; surface area relates to height.

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Spherical Cap Calculator

Spherical Cap

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