In geometry, the radius of a circle or sphere, written as ${\displaystyle r}$,[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 ${\displaystyle {\displaystyle r}}$ and the circumference ${\displaystyle {\displaystyle c}}$ of a circle is ${\displaystyle ~c=2\pi r.}$

The area ${\displaystyle {\displaystyle A}}$ of a circle of radius ${\displaystyle {\displaystyle r}}$ is ${\displaystyle {\displaystyle ~A=\pi r^{2}.}}$

## References

1. "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-24.{{cite web}}: CS1 maint: url-status (link)
2. Weisstein, Eric W. "Radius". mathworld.wolfram.com. Retrieved 2020-09-24.
3. "Radius, diameter, & circumference | Circles (article)". Khan Academy. Retrieved 2020-09-24.