How do you calculate the speed at which a car leaves a curve?

With the formula v = √(g·R·(μ+p)/(1−μ·p)), where R is the radius of the path, μ the lateral friction and p the superelevation. It gives the speed at which the vehicle can no longer hold that curve.

Does vehicle weight affect the critical speed of a curve?

Not for sliding. Mass multiplies equally the force needed to turn and the force the tyre can deliver, so it cancels. It does affect rollover, which is a different phenomenon.

How is the radius of a curve measured from the mark?

With the chord —the straight line between the ends of the measured arc— and the middle ordinate —the maximum separation between that line and the mark—, applying R = c²/(8·m) + m/2. A long chord is worth using, because the radius is very sensitive to errors in the middle ordinate.

Does the car slide off the curve or roll over?

It depends on its geometry. A low car slides before rolling; a tall narrow vehicle may roll before sliding, and then the critical curve speed calculation does not describe what happened.

At what speed does a car run off a curve?

Updated 2026 · 4 min read

A vehicle runs off a curve when the force it needs to turn exceeds the force the tyre can give it. That point has a specific speed —the critical curve speed— and it is calculated from three inputs: the radius, the friction and the superelevation.

The formula

v = √( g · R · (μ + p) / (1 − μ · p) )

Where R is the radius of the path, μ the lateral tyre-road friction and p the superelevation as a fraction. Superelevation adds when the curve is banked inwards and subtracts when it is banked outwards.

Note that mass does not appear. A loaded truck and a small hatchback have the same critical sliding speed on the same curve, because weight multiplies equally the force required and the force the tyre can deliver. What does differ between them is rollover, which is a separate phenomenon.

Where the radius comes from

It is rarely in the road design drawings, and even if it were it would not serve: what matters is the radius of the path the vehicle described, which is not the centreline of the carriageway. It is obtained by measuring the mark left on the asphalt with two quantities:

the chord — the straight line between the two ends of the measured arc;
the middle ordinate — the maximum separation between that line and the mark.

R = c² / (8 · m) + m / 2

A practical warning about the measurement

The middle ordinate is small and the radius is very sensitive to it: an error of one centimetre can move the radius by several metres. It is worth measuring a long chord —the longer the better— and repeating the measurement. If the mark allows two stretches, compute both radii and compare.

Sliding is not rolling over

Critical curve speed says when the vehicle slides. If the vehicle is tall and the track narrow, it may roll over before it slides — and then this calculation does not describe what happened. The comparison is made with the Static Stability Factor, which relates track width to the height of the centre of gravity. A low car always slides before rolling; a tall SUV does not necessarily.

What this calculation does not tell you

It gives the speed at which the vehicle could no longer hold that path. It does not say how fast it was going metres earlier, nor whether the driver braked on entry. If there is a preceding skid mark, the entry speed is higher and the two calculations have to be chained.

Module 12 derives the radius from the chord and the middle ordinate, or takes it directly, and returns the critical speed with the superelevation included.

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Frequently asked questions

How do you calculate the speed at which a car leaves a curve?: With the formula v = √(g·R·(μ+p)/(1−μ·p)), where R is the radius of the path, μ the lateral friction and p the superelevation. It gives the speed at which the vehicle can no longer hold that curve.
Does vehicle weight affect the critical speed of a curve?: Not for sliding. Mass multiplies equally the force needed to turn and the force the tyre can deliver, so it cancels. It does affect rollover, which is a different phenomenon.
How is the radius of a curve measured from the mark?: With the chord —the straight line between the ends of the measured arc— and the middle ordinate —the maximum separation between that line and the mark—, applying R = c²/(8·m) + m/2. A long chord is worth using, because the radius is very sensitive to errors in the middle ordinate.
Does the car slide off the curve or roll over?: It depends on its geometry. A low car slides before rolling; a tall narrow vehicle may roll before sliding, and then the critical curve speed calculation does not describe what happened.

Sources

The transverse friction that decides the critical speed comes from the same published table the braking module uses.

McHenry, R. R. (1976). User’s Manual for the CRASH Computer Program. Calspan ZQ-5708-V-3. Its Exhibit 9-5 lists fourteen surfaces with four pairs of friction values each.

How these methods compare against documented cases is detailed in How this calculator is validated.