Pronunciation: /sfɪər/ Explain

Figure 1: Sphere

A sphere is all points a given distance from a central point in 3-dimensional space.[2] The distance of the surface of the sphere from the center is called the radius.

Equation of a sphere with the center at (0,0,0) x2 + y2 + z2 = r2
Equation of a sphere with the center at (x0, y0, z0) (x - x0)2 + (y - y0)2 + (z - z0)2 = r2
Volume of a spherev = 4/3 π r3
Surface Area of a sphere s = 4 π r2
Table 1: Equations and formulas for spheres

The generalization of a sphere in n-dimensional spaces where n is 4 or more is called a hypersphere. The equation for a four-dimensional hypersphere is (w - w0)2 + (x - x0)2 + (y - y0)2 + (z - z0)2 = r2. A 2 dimensional sphere is called a circle.

Great Circle

A sphere with a great circle and 2 small circles marked.
Figure 2: Sphere showing a great circle and a small circle.

A great circle is a circle on a sphere with the same diameter as the sphere. Circles on a sphere that are not great circles are called small circles. For more information see Great Circle.


Hemisphere: Half of a sphere
Figure 3: Hemisphere

A hemisphere is exactly half of a sphere. A hemisphere can be created using any plane that contains a diameter of the circle.


  1. McAdams, David E.. All Math Words Dictionary, sphere. 2nd Classroom edition 20150108-4799968. pg 168. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pg 50. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 12/13/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/50/mode/1up. Buy the book

More Information

  • McAdams, David E.. Circle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. https://www.allmathwords.org/en/c/circle.html.

Cite this article as:

McAdams, David E. Sphere. 5/7/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/s/sphere.html.

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Revision History

5/7/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/10/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
12/31/2009: Added "References". (McAdams, David E.)
12/5/2008: Changed 'equidistant' to 'a given distance'. (McAdams, David E.)
6/7/2008: Corrected spelling. (McAdams, David E.)
4/1/2008: Initial version. (McAdams, David E.)

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