Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. It is natural to define the curvature of a straight line to be identically zero. The curvature of a circle of radius R should be large if R is small and small if R is large. Thus the curvature of a circle is defined to be the reciprocal of the radius: k = 1/R.

Given any curve C and a point A on it, there is a unique circle or line which most closely approximates the curve near A, the osculating circle at A. The curvature of C at A is then defined to be the curvature of that circle or line. The radius and the centre of this circle are called respectively the radius and center of curvature of the curve C at the point A. The centers of curvature form a curve which is called evolute for the curve C.