By Zencalcy Editorial TeamLast reviewed About us
On a banked curve the road's tilt supplies part of the centripetal force, so less grip is needed to hold a car in the turn. With a frictionless surface there is exactly one speed that needs no sideways friction at all; with tyres, the banking angle and the friction coefficient together set the maximum safe speed.
The speed a banked curve is designed to handle.
| Use 0 for the frictionless design speed. |
v = √(r g (tan θ + μ) / (1 − μ tan θ))
θ is the banking angle and μ the static friction coefficient. With μ = 0 the formula reduces to the familiar frictionless banking relation v = √(r g tan θ).
| Symbol | Meaning |
|---|---|
| v | Design or maximum safe speed, in m/s. |
| r | Radius of the curve, in metres. |
| θ | Banking angle above the horizontal. |
| μ | Static friction coefficient between tyres and road. |
With no friction, v = √(50 × 9.80665 × tan 15°) = 11.46 m/s, or 41.3 km/h. Adding μ = 0.7 raises the maximum to about 24 m/s, roughly 86 km/h.
Continue with the Centripetal Force Calculator, Coefficient of Restitution Calculator, or the Drag Force Calculator — or browse more dynamics tools and all physics calculators.
Above the design speed the car needs more centripetal force than the bank and available friction can supply, so it slides up and out of the curve.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026