View source for Radius

{{For|the human bone|Radius (bone)}}[[File:Radius.PNG|thumb|The radius of a circle]]
In [[geometry]], the '''radius''' of a [[circle]] or [[sphere]], written as <math>r</math>,<ref>{{Cite web|last=|first=|date=2020-04-17|title=List of Geometry and Trigonometry Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/geometry-trigonometry-symbols/|archive-url=|archive-date=|access-date=2020-09-24|website=Math Vault|language=en-US}}</ref> is the shortest connection between the center and the boundary. It is either the distance from the center to the [[perimeter]] (in the case of a circle), or the distance from the center to the [[surface]] (in the case of a sphere). It is half of the [[diameter]].<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Radius|url=https://mathworld.wolfram.com/Radius.html#:~:text=The%20distance%20from%20the%20center,equal%20to%20half%20the%20diameter.|access-date=2020-09-24|website=mathworld.wolfram.com|language=en}}</ref> That is, when ''r'' is the radius and ''d'' is the diameter:<ref>{{Cite web|title=Radius, diameter, & circumference {{!}} Circles (article)|url=https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-area-circumference/a/radius-diameter-circumference|access-date=2020-09-24|website=Khan Academy|language=en}}</ref>

''r'' = ''d'' ÷ 2

''d'' = 2 x ''r'' = ''r'' + ''r''

The relationship between the radius <math>{\displaystyle r}</math> and the [[circumference]] <math>{\displaystyle c}</math> of a circle is 
<math>~c = 2\pi r.</math>

The [[area]] <math>{\displaystyle A}</math> of a circle of radius 
<math>{\displaystyle r}</math> is 
<math>{\displaystyle ~A = \pi r^2.}</math>

==Related pages==
* [[Area]]
* [[Covalent radius]]
* [[Diameter]]
* [[Radian]]

== References ==
<references />

== Other websites ==
* [http://www.mathopenref.com/radius.html Definition and properties of the radius of a circle] with interactive applet


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[[Category:Geometry]]