Ideal Banking Angle Calculator

Reviewed By: Patrick Myers (BSME)

Enter the velocity, radius, and gravitational acceleration into the calculator to determine the ideal banking angle for a curve.

Frictionless (Ideal)

With Friction (Safe Speed Range)

Enter any 3 values to calculate the missing variable

Banking Angle

Velocity

Radius

Gravitational Acceleration

Ideal Banking Angle Formula

The following formula is used to calculate the ideal banking angle for a given velocity, radius, and gravitational acceleration.

θ = atan((v²) / (r * g))

Variables:

θ is the banking angle in degrees
v is the velocity in meters per second (m/s)
r is the radius of the curve in meters (m)
g is the gravitational acceleration in meters per second squared (m/s²)

To calculate the ideal banking angle, divide the square of the velocity by the product of the radius and gravitational acceleration, then take the arctangent of the result.

What is an Ideal Banking Angle?

The ideal banking angle is the angle at which a road or track should be banked (tilted) to allow vehicles to travel around a curve at a specific speed without relying on friction. This angle ensures that the centripetal force required to keep the vehicle on the curved path is provided by the normal force, reducing the risk of skidding. The ideal banking angle depends on the speed of the vehicle, the radius of the curve, and the gravitational acceleration.

How to Calculate Ideal Banking Angle?

The following steps outline how to calculate the Ideal Banking Angle.

First, determine the velocity of the vehicle (v).
Next, determine the radius of the curve (r).
Next, determine the gravitational acceleration (g), typically 9.81 m/s².
Finally, calculate the ideal banking angle using the formula θ = atan((v²) / (r * g)).
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Velocity (v) = 20 m/s

Radius (r) = 50 m

Gravitational Acceleration (g) = 9.81 m/s²

Follow-Up Calculations

On a 300 m-radius highway curve, the ideal banking angle at 60 mph is about 14°, which works out to roughly 0.24 g of lateral acceleration. For a 3,300 lb car, that is about 300 lb of load shifting across the chassis, and the weight shift on each axle shows how that cornering force redistributes from the inside tires to the outside tires.

If a turn is banked for 60 mph but you enter it at 70 mph, the road no longer supplies exactly the right centripetal force and the tires have to pick up the difference. You can use the slip angle for a corner to estimate how much the car will start to push or drift when your speed does not match the curve’s ideal banking.

In the same 300 m curve at 60 mph, a 3,300 lb vehicle needs about 800 lb of total lateral force to follow the path, and the bank angle helps the road carry part of that load. The force at each wheel is useful for seeing how much work each contact patch is doing when you compare a flat turn to a properly banked one.