Radius of Curvature Calculator

About this calculator

Curvature (κ) measures how sharply a curve bends at a point — a tight turn has high curvature, a nearly straight path has curvature close to zero. The radius of curvature is simply its reciprocal, R = 1/κ: it's the radius of the circle that best hugs the curve at that exact point, so a small radius means a sharp bend and a large radius means a gentle one.

This relationship is used across physics and engineering — optical engineers use it to describe lens and mirror surfaces, structural and highway engineers use it to design safe road and rail curves, and mechanical engineers use it in beam-bending and cam-profile calculations. Enter a curvature value in inverse meters (1/m) to get the corresponding radius.