Banked Curve Calculator

About this calculator

This calculator finds the ideal (frictionless) banking angle for a curve at a given radius and design speed, using θ = arctan(v²/rg), where v is speed, r is the curve's radius, and g is gravitational acceleration. At this angle, the horizontal component of the normal force alone supplies the centripetal force needed to turn, with no reliance on friction — meaning a vehicle could take the curve at that exact speed even on ice.

Civil and highway engineers use this formula when designing banked roads, racetrack turns, and railway curves to set a safe superelevation for the intended speed, since taking a curve too fast for its banking pushes a vehicle outward (relying on friction to compensate) while taking it too slow can pull it toward the inside edge. Enter the radius and design speed to get the ideal banking angle.