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# Radius

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For the human bone, see Radius (bone).

In geometry, the **radius** of a circle or sphere, written as [math]r[/math],^{[1]} 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.^{[2]} That is, when *r* is the radius and *d* is the diameter:^{[3]}

*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

## References

- ↑ "List of Geometry and Trigonometry Symbols" (in en-US). 2020-04-17. https://mathvault.ca/hub/higher-math/math-symbols/geometry-trigonometry-symbols/.
- ↑ Weisstein, Eric W.. "Radius" (in en). https://mathworld.wolfram.com/Radius.html#:~:text=The%20distance%20from%20the%20center,equal%20to%20half%20the%20diameter..
- ↑ "Radius, diameter, & circumference | Circles (article)" (in en). https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-area-circumference/a/radius-diameter-circumference.

## Other websites

- Definition and properties of the radius of a circle with interactive applet