Maximum Cornering Speed Calculator (Curve Radius, Grip & Banking)
Find the maximum speed a car can take a curve from its radius, the road grip and the banking (superelevation) — v = √(g·r·(μ + e) ÷ (1 − μe)) — with the AASHTO highway formula and lateral g.
How it works
v = √(g × r × (μ + e) ÷ (1 − μ × e)) · v in m/s, r in m, μ = tyre–road friction, e = superelevation as a decimal (tan of the bank angle) · AASHTO highway form: V = √(127 × R × (e + f)) km/h with R in m, or V = √(15 × R × (e + f)) mph with R in ft
A car can corner only as fast as the tyres can supply the centripetal force. On a flat road that limit is friction alone, v = √(μgr); banking the road helps because part of the car's weight then pushes it toward the centre of the turn. The AASHTO design formula is the same balance with the small μ·e term dropped and uses low "side friction" factors (about 0.10–0.17) for comfort, while the skid-limit values here (0.7 on dry asphalt) show the speed at which tyres actually let go. Real limits also depend on tyres, load transfer and road roughness.
Worked example
A flat curve with a 100 m radius on dry asphalt (μ = 0.70): v = √(9.81 × 100 × 0.70) = 26.2 m/s, which is 94 km/h (59 mph). The AASHTO form gives the same √(127 × 100 × 0.70) = 94 km/h. On a wet road (μ = 0.40) the limit falls to about 71 km/h.
Sources: AASHTO horizontal curve design — minimum radius e + f relationship (FHWA) · HyperPhysics — Banked curve
Frequently asked questions
How do you calculate the maximum speed on a curve?
On a flat road, v = √(μ × g × r). For a 100 m radius on dry asphalt (μ ≈ 0.7) that is √(0.7 × 9.81 × 100) ≈ 26 m/s, or about 94 km/h. Add the superelevation for a banked curve.
Why are posted curve speeds so much lower?
Advisory speeds use comfortable side-friction factors of about 0.1–0.17 so drivers feel little sideways push and have a large margin for wet roads, worn tyres and mistakes. The skid limit is far higher than a safe driving speed.
How much does road banking help?
Each 1% of superelevation adds roughly 0.01 to the effective friction. A 6% bank on a 100 m curve raises the dry-road limit from about 94 to 100 km/h, and helps more on slippery roads where friction is low.
Does a heavier car corner slower?
In this simple model mass cancels out. In reality heavier cars and high centres of gravity transfer more load to the outside tyres, which reduces the usable grip slightly.
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This calculator is for educational purposes. Double-check important results before acting on them.