Banked Curve Speed Calculator

About this calculator

A banked curve tilts the road surface inward so that part of the normal force from the road points toward the center of the turn, helping supply the centripetal force needed to keep a vehicle moving in a circular path. At the ideal speed for a given bank angle, the horizontal component of the normal force alone provides exactly enough centripetal force — no friction from the tires is needed at all, which is why this speed is also called the "no-friction" or design speed of the curve.

This calculator finds that ideal speed from the curve's radius and bank angle using v = √(r·g·tanθ), derived by setting gravity, the normal force, and the required centripetal force in balance. It's the formula behind how civil and highway engineers set banking angles on highway ramps and racetracks, and it's a standard example in introductory physics courses covering circular motion and Newton's laws.