Spherical Zone Area and Volume Calculator


Online Spherical Zone Area and Volume Calculator: Calculate the volume and area of a Spherical Zone based on its height, small radius, large radius and r the radius. Enter four unknowns in the form and press the CALCULATE button.

Table of contents:

What is a Spherical Zone?

A spherical zone is the portion of the surface of a sphere between 2 parallel planes which intersect this sphere. When one of the planes is tangent to the sphere, the area is called a spherical cap. When one of the planes is tangent to the sphere and the other plane passes through the center, the area is called the hemisphere. A hemisphere is half of a sphere.

The characteristics of the Spherical Zone

The height of the spherical part is the perpendicular distance between the 2 bases. It is denoted by h.

The bases of the zone are the circumference of the sections made by the 2 parallel planes.

If one of the bounding parallel planes is tangent to the sphere, the surface bounded is a zone of one base.

Calculate the area of a Spherical Zone

The area of a spherical zone or of a spherical cap is given by the following formula:

A = 2π .r .h

in which :

r is the radius of the sphere;

h is the distance between the two parallel planes.

Calculate the volume of the Spherical Zone

The volume V of a spherical Zone corresponding to a spherical cap of height h in a ball of radius r is given by the relationship:

V = π h / 6 (3R2 + 3r2 + h2)

in which :

h: height of the zone

a: large radius

b: small radius