Spherical Sector Area and Volume Calculator


Online Spherical Sector Area and Volume Calculator: Calculate the volume and area of a Spherical Sector based on its height and r the radius. Enter two unknowns in the form and press the CALCULATE button.

Table of contents:

What is a Spherical Sector?

If a radius of a sphere moves along a small circle of the sphere as a guide curve, it describes a conical surface and divides the corresponding ball into two spherical sectors, one minor and the other major.

The term spherical sector generally designates the salient sector, that is to say that of the two sectors which is convex. This sector can be described as the meeting of a spherical cap and the cone whose apex is at the center of the sphere and the base corresponds to the base of the spherical cap.

The characteristics of the Spherical Sector

More precisely, the half-cone cuts two solids in the ball, one convex, the volume of which is less than a half-ball is called a minor sector, the other is called a major sector. It is the minor sector which is commonly called the spherical sector.

The base of spherical sector is its zone.

Do not confuse: so-called ball sector valves in plumbing are in reality made up using a portion of a hollow sphere close to a spherical spindle.

Calculate the total area of a Spherical sector

The total area A of a spherical sector of radius R of height h in a ball of radius r is given by the following formula:

A = 2π .r .h + π . R . r = π . r (2h + R).

Calculate the volume of the Spherical sector

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

V = (2 . π .r2 .h)/3