Frictionless Banked Curve Calculator
Enter gravity, curve radius, speed, and bank angle to calculate the ideal speed and angle relationship.
Ideal frictionless relation: tanθ = v²/(rg). Speed = √(rg tanθ); angle = atan(v²/(rg)). Educational relation only; not road-safety guidance.
All calculations run in this browser; values are not uploaded or saved.
Reference: OpenStax College Physics 2e
Enter values to calculate.
A QUICK WALKTHROUGH
How to use this tool
- Enter gravity g and curve radius r using the displayed units.
- Enter speed v and bank angle θ; the tool calculates both corresponding outputs.
- Review the idealized results and their limits.
Idealized relationship
The calculator uses tanθ = v²/(rg): speed = √(rg tanθ), and angle = atan(v²/(rg)). It assumes an ideal frictionless curve and does not model tire friction or road conditions.
Educational scope and privacy
This physics relationship is for learning, not road-safety guidance or a design recommendation. Calculations run in this browser; values are not uploaded or saved.
GOOD TO KNOW
Common questions
What does each result calculate?
The tool calculates the ideal speed corresponding to the entered bank angle and the ideal angle corresponding to the entered speed.
Can I use this to choose a safe road speed?
No. The frictionless model omits real road and vehicle conditions and is not safety guidance.