Banked Turn Angle Calculator
A banked curve lets a vehicle turn safely without depending on tyre friction by tilting the road so that the normal force supplies the centripetal force. The ideal banking angle depends only on the speed, the radius of the turn, and gravity, not on the vehicle's mass. This calculator uses the centripetal force balance to find the banking angle, taking the speed and turn radius with an editable gravitational acceleration, and returns the angle in degrees along with the required centripetal acceleration.
Banking angle formula
tan(theta) = v^2 / (r * g)
theta = arctan( v^2 / (r * g) ) in degrees
Centripetal acceleration = v^2 / r
The mass cancels from the force balance, so the angle depends only on speed, radius, and gravity. The banking angle rises with the square of the speed and falls as the radius or gravity increases.
Banked turn facts
- The ideal angle needs no friction to hold the vehicle in the turn.
- The banking angle is independent of vehicle mass.
- Doubling the speed roughly quadruples the tangent of the angle.
- Larger radius curves need less banking at the same speed.
- Below the design speed, friction must act up the slope; above it, down the slope.
Banked turn angle: frequently asked questions
What is the ideal banking angle?
The ideal banking angle is the slope at which a vehicle can round a curve at a given speed with no reliance on friction. The horizontal component of the normal force alone supplies the centripetal force. The angle satisfies tan(theta) = v squared divided by (radius times g).
How is the banking angle formula derived?
Setting the horizontal component of the normal force equal to the required centripetal force m v squared over r, and the vertical component equal to the weight m g, the mass cancels and gives tan(theta) = v squared / (r g). The angle is the inverse tangent of that quantity.
Does the banking angle depend on the vehicle mass?
No. The mass cancels out of the equation, so the ideal banking angle for a given speed and radius is the same for a car, a truck, or a cyclist. This is why a single banked road serves vehicles of very different weights.
What speed is a banked curve designed for?
A banked curve is built for one design speed at which no friction is needed. Below that speed, friction must point up the slope to prevent sliding inward; above it, friction must point down the slope to prevent sliding outward. The design speed corresponds to the angle this calculator returns.
What value of gravity should I use?
Standard gravity is 9.80665 metres per second squared. This calculator exposes g as an editable input so you can use a local value. The banking angle increases with the square of the speed and decreases with larger radius or stronger gravity.
Official sources
- NIST: Standard acceleration of gravity.
- U.S. Federal Highway Administration: Highway geometric design and superelevation.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.