Área Segmento Esférico
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
A = 2πRh
About this calculator
The spherical segment area calculator determines the surface area of a spherical cap, which is the part of a sphere cut by a plane. The calculation uses the formula A = 2πRh, where R is the sphere's radius and h is the segment height. This area corresponds to the curved surface of the cap, excluding the flat base.
To use the tool, enter the sphere's radius (R) and the segment height (h). The height must be less than or equal to the sphere's diameter. The result is the curved surface area in square units. It is useful in spatial geometry problems, engineering, and design, such as calculating materials for domes or spherical tanks.
Cautions: ensure the height does not exceed the diameter, as this would result in an invalid segment. Also, the formula only considers the lateral area, not the base. If you need total area, add the base area (πr², where r is the base radius of the segment). Verify that R and h are in the same units.
Use cases: calculating the area of a hemispherical dome (h = R), the painted area of a partially filled spherical tank, or the area of a segment in physics and astronomy problems. The tool simplifies these calculations with accuracy.
Frequently asked questions
What is the difference between a spherical segment and a spherical cap?
A spherical segment is the region of a sphere cut by a plane, including the circular base. A spherical cap is the curved surface of that segment, without the base. The formula A = 2πRh calculates the cap area.
Can I use the calculator for a hemisphere?
Yes, for a hemisphere (h = R), the cap area is 2πR², which is half the total sphere area (4πR²). The calculator returns this value.
What if the height is greater than the radius?
The height can be greater than the radius, but must not exceed the diameter (2R). If h > 2R, the segment does not exist. The calculator should validate this.
How do I calculate the total area of the spherical segment?
Total area is the cap area (2πRh) plus the base area (πr²), where r is the base radius. r can be calculated as r = √(h(2R - h)).
Does the formula work for any height?
Yes, for 0 ≤ h ≤ 2R. If h = 0, area is zero (point). If h = 2R, area is 4πR² (full sphere).