Área calota esférica

2πRh.
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

A
62,8319

About this calculator

The spherical cap area calculator determines the surface area of a portion of a sphere cut by a plane. This tool is useful in engineering, architecture, and design projects where spherical sections need precise measurements. The formula uses the sphere's radius (R) and the cap's height (h) to compute the curved surface area of the cut section.

The formula 2πRh is derived from spherical geometry and accounts for the sphere's curvature. Simply input the sphere's radius and the cap's height to calculate the surface area. For instance, if a spherical tank has a 5 cm tall opening, the calculator provides the exposed surface area. Ensure all measurements use consistent units (meters, centimeters, etc.) to avoid errors.

This tool is critical for manufacturing spherical components in automotive and packaging industries, where surface area accuracy affects costs and performance. If the cap is small (h ≈ 0), the calculated area will proportionally decrease. Conversely, a large cap (h ≈ 2R) covers a significant portion of the sphere.

Note: the calculator assumes a perfect spherical cap. Real-world objects with imperfections or deformations may require manual adjustments. Always verify units and the object's symmetry before applying results.

Frequently asked questions

What is a spherical cap?

It is a portion of a sphere bounded by a plane, forming a curved 'cap'. Examples include openings in spherical tanks or geodesic structures.

What measurements are required for the calculation?

You need the sphere's radius (R) and the cap's height (h). Both measurements must use the same units (e.g., meters).

Does the formula work for any cap height?

Yes, as long as 0 < h ≤ 2R. If h = R, the cap corresponds to half a sphere.

How is cap height related to the sphere's radius?

The height (h) is the distance between the cap's top and the cutting plane. If the plane passes through the sphere's center, h = R.

Other Geometria Esférica calculators