File:CIRCLE 1.svg
Circle illustration

In classical geometry, a radius (plural: radii) of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment. The radius is half the diameter. In science and engineering the term radius of curvature is commonly used as a synonym for radius.

More generally—in geometry, engineering, graph theory, and many other contexts—the radius of something (e.g., a cylinder, a polygon, a graph, or a mechanical part) is the distance from its center or axis of symmetry to its outermost points. In this case, the radius may be more than half the diameter.

The relationship between the radius and the circumference of a circle is ${\displaystyle r={\frac {c}{2\pi }}}$.

To compute the radius of a circle going through three points ${\displaystyle P_{1},P_{2},P_{3}}$, the following formula can be used:

${\displaystyle r={\frac {|P_{1}-P_{3}|}{2\sin(\theta )}}}$

where ${\displaystyle \theta }$ is the angle ${\displaystyle \angle P_{1}P_{2}P_{3}.}$