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 (e.g., Lawrence 1972, p. 4).

Let
and
be given parametrically by

(2)

(3)

then

(4)

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