The radius of a circle is the distance from the center to any point on the circle. Identical definitions hold for the sphere and hypersphere. The plural form of radius is radii.

The radius of a circle is often denoted using R or r.

$[asy]size(150); pair O=origin, P=dir(30); D(unitcircle); D(O--P); MP("O",D(O),NNW); MP("P",D(P),NE); MP("r",midpoint(O--P),NNW);[/asy]$

## Links to other key terms

1. diameter: $d = 2 r$

The diameter is the longest chord is a circle. It is usually expressed by D or d.

2. circumference (perimeter): $C = 2 \pi r$

The circumference is the distance around a circle. It is usually represented by C.

3. area: $S = \pi r^2$

The area of a circle is the amount of space it occupies. It is usually denoted using S or A.

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