Hemisphere Calculator

Name: Hemisphere - Geometry Calculator
Author: Jürgen Kummer

Calculations at a hemisphere. A hemisphere is a sphere halved in the middle. Radius and diameter refer to the original sphere. The calotte is the curved part of the hemisphere.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

d = 2 r

A = 3 π r^{2}

A_{K} = 2 π r^{2}

V = \frac{2}{3} π r^{3}

\frac{A}{V} = \frac{9}{2 \cdot r}

pi:

π = 3.141592653589793...

Radius and diameter have the same unit (e.g. meter), areas have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The base of the hemisphere is a circle. The vertical cross-section forms a semicircle. If you halve a hemisphere twice, each time vertically, you get a spherical corner. A halved spherical shell becomes a half spherical shell. A straight circular cylinder with a matching hemisphere placed on its two flat sides is a capsule. A straight cut through a sphere that does not go through the center does not divide it into hemispheres, but into two spherical caps.
The hemisphere is axially symmetrical to every plane in which the perpendicular bisector lies and rotationally symmetrical to this perpendicular bisector for every angle. It is not point symmetrical.
The term "hemisphere"h is also often used to distinguish two parts of non-spherical objects. The Earth, which is an almost spherical oblate spheroid, is referred to as a northern and southern hemisphere, and less frequently as an eastern and western hemisphere. The celestial sphere is also divided into hemispheres; here, the "sphere" is simply the shape onto which images are projected. The left and right halves of the brain are also sometimes referred to as hemispheres.

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