The radius of curvature is given by

(1) 
where is the Curvature. At a given point on a curve, is the radius of the Osculating Circle.
The symbol is sometimes used instead of to denote the radius of curvature.
Let and be given parametrically by
then

(4) 
where and .
Similarly, if the curve is written in the form , then the radius of curvature is given by

(5) 
See also Bend (Curvature), Curvature, Osculating Circle, Torsion (Differential Geometry)
References
Kreyszig, E. Differential Geometry. New York: Dover, p. 34, 1991.
© 19969 Eric W. Weisstein
19990525