Banked Curve Angle Calculator
Find the ideal (frictionless) banking angle of a road or track curve from the design speed, turn radius and gravity.
How it works
tan θ = v² ÷ (r·g) · θ = arctan(v² ÷ (r·g))
On a frictionless banked curve the horizontal component of the normal force supplies all the centripetal force, so the road is tilted until tan θ equals v²/(rg). At exactly the design speed a vehicle rounds the curve needing no sideways grip at all. Notice mass drops out entirely — a loaded truck and a light car want the same banking angle — and the angle rises steeply with speed but falls as the radius grows.
Worked example
A curve of radius 100 m designed for 25 m/s (90 km/h) with g = 9.81 m/s²: tan θ = 25² / (100 × 9.81) = 625 / 981 = 0.637, so θ = arctan(0.637) ≈ 32.5°. Below this speed friction must act down the slope; above it, up the slope.
Sources: Banked turn — Wikipedia
Frequently asked questions
Does a heavier vehicle need a different banking angle?
No. Mass cancels out of tan θ = v²/(rg), so the ideal angle depends only on speed, radius and gravity. Every vehicle at the design speed rounds a frictionless banked curve the same way.
What happens if you drive faster or slower than the design speed?
The banking is perfect only at the design speed. Drive slower and friction must point down the incline to stop you sliding in; drive faster and friction must point up the incline to stop you sliding out.
Why are racetrack and highway curves banked?
Banking lets the normal force do part of the turning job, reducing the sideways friction the tyres must provide. That allows higher safe cornering speeds and makes the turn less dependent on road grip in rain or ice.
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This calculator is for educational purposes. Double-check important results before acting on them.