The radius of curvature formula is denoted as 'R'. The radius of curvature is not a real shape or figure rather it's an imaginary circle. Let us learn the radius of curvature formula with a few solved examples. For sign convention, the second derivative ( ′′) corresponds to the curvature or concavity of the graph. For upward concave curves, the second derivative is positive, therefore curvature is also positive; while for downward concave curves, the second derivative and curvature are negative. Example1 Find the radius of curvature at the point = of the curve = 4 sin − sin 2 Learn what is the radius of curvature of a curve, how to calculate it using different parametrizations and coordinates, and see examples and references. The radius of curvature is the reciprocal of the curvature and the radius of the osculating circle. Definition 1.3.1 The circle which best approximates a given curve near a given point is called the circle of curvature or the osculating circle2 at the point. The radius of the circle of curvature is called the radius of curvature at the point and is normally denoted \ (\rho\text {.}\) The curvature at the point is \ (\kappa=\frac {1} {\rho}\text {.}\) The centre of the circle of curvature is called centre of curvature at the point.
