Nominally, a polished ferrule will have a dome-shaped surface, permitting two coupled ferrules to come into contact over a small surface area in the region of the fiber. A small radius of curvature indicates a smaller contact area between the ferrules. Radius of curvature for a UPC connector should fall between 7 and 25mm, whereas for an APC connector, the range of acceptable radii is from 5 to 12mm.
The distance from the center of a sphere or ellipsoid to its surface is its radius. The equivalent "surface radius" that measures distances along the body's surface is its radius of curvature (more formally, the radius of curvature of a curve at a point is the radius of the osculating circle at that point). With a sphere, the radius of curvature equals the radius.
Radius of curvature has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located in (x, y, z) either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis.