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 $r=\backslash frac\{c\}\{2\backslash pi\}$.

To compute the radius of a circle going through three points $P\_1,\; P\_2,\; P\_3$, the following formula can be used:

$r=\backslash frac\{2\backslash sin\backslash theta\}$

where $\backslash theta$ is the angle $\backslash angle\; P\_1\; P\_2\; P\_3.$

A more simple way to find the length of the radius is:

$r=\backslash frac\backslash text\{diameter\}\{2\}.$

A radius may also be applied to arithmetic. Where 4,5,6,7,8,9 and 10 can be in a three number radius of 7.

Polygons

Regular polygons are sometimes said to have a radius, defined as the distance from the center to a vertex. This is the same as the radius of a circumscribed circle with the same center. This latter formulation is sometimes used to define the radius of an arbitrary polygon and is called the circumradius.

The radius of the minimum bounding circle that completely contains a polygon is called ... . The minimum bounding circle is the same as the circumscribed circle for regular polygons, but is often different for irregular polygons.

The inradius or filling radius of a given perimeter is the radius of the inscribed circle -- the largest circle that will fit inside that perimeter.

See also

• Radius (bone)
• Radius of convergence
• Filling radius (Riemannian geometry)