ArcCurvature

ArcCurvature[{x1, ..., xn}, t] gives the curvature of the parametrized curve whose Cartesian coordinates xi are functions of t.

ArcCurvature[{x1, ..., xn}, t, chart] interprets the xi as coordinates in the specified coordinate chart.

Examples

Find the curvature of a circle:

ArcCurvature[{Cos[t], Sin[t]}, t]
(* 1 *)

Curvature of a helix:

ArcCurvature[{Cos[t], Sin[t], t}, t]
(* 1/2 *)

Please visit the official Wolfram Language Reference for more details.