In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point.

The curvature (K) of a path is measured using the radius of the curvature of the path at the given point. If y = f (x) is a curve at a particular point, then the formula for curvature is given as K = 1/R.

Jul 23, 2025 · The radius of curvature of a curve is defined as the approximate radius of a circle at any given point or the vector length of a curvature. It exists for any curve with the equation y = f (x) with x …

The radius of curvature of the curve at a particular point is defined as the radius of the approximating circle. This radius changes as we move along the curve.

The radius of curvature formula is R = (1 + (dy/dx)^2)^ (3/2)/|d²y/dx²|. It measures the curvature of a curve at a point, considering its slope and second derivative.

As promised, the curvature, \ (\kappa\), of a circle is the reciprocal of its radius, \ (R\). Based on this fact, we define: The radius of curvature of a curve is the reciprocal of its curvature: \ [ R=\dfrac {1} {\kappa} \]

The center of curvature and the tangent vector to the curve, T (t), determine a plane called the plane of curvature. Since the radius of a circle is always normal to a vector tangent to it, a line from r (t) …