Banked Curve Calculator
The banking angle a curve needs so a vehicle holds the corner without relying on friction — and the speeds friction then allows.
On a frictionless banked curve the ideal speed satisfies tan θ = v²/(rg).
How the banked curve calculator works
On a frictionless banked curve the ideal speed satisfies tan θ = v²/(rg). Bank it for that speed and the road pushes the car round the corner with no sideways grip needed at all.
Friction then widens the range: the same bank holds a band of speeds, and the width of that band is what makes a banked road forgiving. It is why motorway curves are banked and why a velodrome is banked so steeply.
Formula: tan θ = v² / (r g)
Worked examples
| Inputs | Ideal bank angle (degrees) | Note |
|---|---|---|
| 100 km/h on a 250 m curve | 17.4702 | 17.5° ideal bank |
| A tighter curve | 44.524 | a much steeper bank |
| A slow corner | 2.8828 | barely needs banking |
FAQFrequently asked questions
Why are roads banked?
So the road surface itself provides part of the cornering force, which means the corner holds even when grip is poor — in rain, or on ice.
What is the ideal speed on a banked curve?
The speed at which no sideways friction is needed at all. Above it you slide out, below it you slide in — and friction covers both up to a point.
Why are velodromes banked so steeply?
Small radius and high speed. The tan relationship means a 25 m radius at 60 km/h needs about 55 degrees.
How much lateral g can a car hold?
A road car on dry tarmac holds around 0.8 to 0.9 g. Wet halves it, which is why banking matters so much.
Does banking help a truck?
It helps the grip but a high centre of mass can still roll before it slides. Banking changes the sliding limit, not the tipping one.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.