Volume of the ball segment

To find the volume of a spherical segment, it is enough to remember one simple formula that includes two unknown parameters (if we count together with pi – three). But first, let’s remember what each word of the designated concept describes.


Calculate the volume of the ball segment

Enter the radius of the ball R
Enter the height value h

Formulas and definitions

Volume (from lat. volume – “filling”) is a quantitative characteristic of the space occupied by a body or substance.

A ball (i.e., a geometric body) is a collection of all points of space that are located in it from the center at a certain distance (read. in a certain distance; it is also considered its radius), which appears to be no more than the value set for it.

The segment here denotes a certain “limitation” in the space of the corresponding form.

In other words, it is a part of the [volume] of the ball (it also appears to be a kind of geometric body), which is cut off from it by a plane (i.e., bounded by a spherical segment (read. the surface of the spherical part of the spherical segment) and a circle formed in the cross section and is the basis of the considered “limitation”; at the same time, their boundaries coincide). Every plane that intersects the ball divides it into exactly two segments (if it passes through the center, then such segments are called hemispheres).

The formulas for calculating the volume of the ball segment are as follows, to choose from:

Формулы для расчета шарового сегмента


h – is the height of the ball segment,

R – is the radius of the [large circle] of the ball;

the number π is a mathematical constant equal to 3.14.