Radius

The radius of a circle

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

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