Lateral Acceleration Calculator

Speed (v)

Turn radius (r)

Lateral acceleration (a)

Enter the speed and the turn radius to get the lateral acceleration, or fill any two of the three fields and leave the unknown blank. Switch the acceleration field to g to read the answer in g-force.

Show rotational motion

Treat the curve as part of a full circle and add the angular velocity, the period of one lap, and the revolutions per minute.

Add cornering force

Enter a mass to get the centripetal (lateral) force that holds it on the curve, F = m a.

Add road and track dynamics

Banking angle for a frictionless curve, the grip the tires need, and the fastest speed your available grip allows for this radius.

Please input values into the fields

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Show the speed-sensitivity chart

Plot how lateral acceleration climbs with the square of speed for your radius, with a matching speed table.

Show the benchmark comparison

Compare your corner's g-force against an economy car, a sports car, race slicks, and an F1 car.

Lateral acceleration is the sideways force that an object experiences when it turns. In the case of a car this is the force which presses you against the door when driving around a high speed corner and also why the tires try to stay on the road. This calculator computes the lateral acceleration from velocity and turning radius, showing both results in meters per second squared as well as g-force. It can also be used in reverse; if you enter a target g-force and a radius, it will compute the maximum speed at which that corner can be taken. And if you enter velocity and acceleration, it will calculate the radius.

What is lateral acceleration?

Essentially, the lateral acceleration is a centripetal force. When an object moves along a curve, its velocity direction changes constantly and this change in velocity creates an acceleration. This acceleration acts directly towards the center of the curve. The larger the value, the more strongly the object will be pulled toward the center of the curve.

Many people express this in units of "g". One "g" is equal to 9.80665 meters per second squared and is the same acceleration felt when standing still under the influence of gravity. Most passenger cars on dry pavement typically achieve about 0.7 to 0.9 g before their tires begin to slip. Sports cars with high-grip tires can achieve over 1 g. Formula One race cars generate lateral accelerations of more than 5 g while driving through fast corners, due mainly to the aerodynamic downforce that presses the tires firmly against the road.

Formula for calculating lateral acceleration

The lateral acceleration is directly derived from the circular motion. It is the result of dividing the square of the speed by the curve radius.

a = \frac{v^2}{r}

Here "a" is the lateral acceleration, "v" is the speed along the track and "r" is the radius of the curve. The square of "v" is important. If the speed doubles, the acceleration quadruples. To express the result as a g-force, divide by standard gravity.

a_g = \frac{v^2}{r \times 9.80665}

Example calculation:

Let's take a car that is driving around a curve with a radius of 50 meters at a speed of 72 kilometers per hour, or 20 meters per second.

a = \frac{20^2}{50} = \frac{400}{50} = 8\ \text{m/s}^2

To convert this to a g-value divide 8 by 9.80665 which gives approximately 0.82g. This is within the range of limits that a typical road tyre can achieve on dry tarmac. If the car were to take the same corner at five km/h faster, then it would exceed this limit. This is the effect of the square of the speed.

How to use this calculator:

Enter the speed and turning radius, select units if necessary, then check the lateral acceleration in the results area. If you switch the acceleration field to 'g', you can read off the g-value directly.

If you want to calculate the other sizes just leave the corresponding fields blank. If you enter the radius and target acceleration then you will get the speed; if you enter the speed and acceleration then you will get the radius. It is not necessary to select a mode as leaving fields blank tells the tool what you want to calculate.

Calculating speed or radius:

This relationship contains three quantities and since there is only one equation you can manipulate it to find any of these quantities.

v = \sqrt{a\,r} \qquad r = \frac{v^2}{a}

Thus, if you specify a comfortable lateral g-value for the occupants and give the radius, then using the first formula you can calculate the speed required to achieve that g-value. This is the method used in designing curves on public roads based on a target value. Using the second formula, given measured speed and acceleration, you can work back to find the radius. Such an approach is often used in accident reconstruction.

Rearranging the equation:

This table shows the same relationship in three forms, each corresponding to one of the three missing quantities.

To find	Formula	In words
Lateral acceleration	a = v squared / r	Speed squared over the radius
Speed	v = square root of (a r)	Square root of acceleration times radius
Radius	r = v squared / a	Speed squared over the acceleration

g-value, adhesion, friction limit

The g-value is not just a subjective feeling but gives the exact grip required by the tyre. On flat roads the lateral g-value corresponds to the minimum coefficient of friction that the road must offer. For curves producing a lateral acceleration of 0.82g, a coefficient of friction between the tyres and the road surface of at least 0.82 is required. If the lateral acceleration exceeds this limit, then the tyre loses grip and the vehicle immediately skids out. Whether it understeers or oversteers depends on which side first loses grip.

If a curve is banked (inclined) inward, it helps to direct the force of gravity toward the center of the vehicle, allowing the vehicle to go around the curve with less traction. Ideally no traction would be needed at all. For this reason, banking is used on race tracks, bicycle racing courses and highway on-ramps. By opening the "Road & Track Dynamics" tab you can check the required bank angle for when no friction force is needed, the amount of grip required for a flat road, and the maximum allowable speed based on current grip for that radius.

Does mass have an impact on the result?

No, it does not affect the g-value itself. The lateral acceleration depends only on speed and radius. A fully loaded truck vehicle and a small go-kart both reaching the same g-value will experience the same lateral force. Mass only plays a role in forces. The centripetal force required to keep an object moving in a curve is equal to the product of the mass of the object and its lateral acceleration.

F = m\,a = \frac{m\,v^2}{r}

A heavier object requires a proportionally greater force to maintain the same path, so heavier vehicles also put more stress on tires at the same g-value. You can check these forces by opening the "Cornering Forces" tab and entering mass.

Situations where lateral acceleration occurs:

Vehicle dynamics engineers measure the maximum lateral g-value to compare tire compound properties, suspension tuning and body rigidity. Road planners use this formula in reverse, first selecting a comfortable lateral g-value for passengers and then determining the corresponding curve radius and banking angle.

Racing teams analyze the lateral g-values of a vehicle's telemetry data in detail to find out where time is still being lost. Accident investigators deduce from brake marks and the geometry of the curve whether the vehicle has exceeded its grip limit before it left the road. Automatic driving systems also treat lateral g-values as strict restrictions when planning the vehicle route through a curve, since passengers do not like strong sideways movements very much.

Assumptions and limitations:

The basic calculation assumes that the road is flat and level, and that the vehicle is travelling at a constant speed and turning in an arc of a constant radius. On banked corners, the grip required by the tyres is reduced, and at the actual entry and exit points of the corner there are transient loads due to weight transfer which this formula does not take into account.

Actual grip is determined by the condition of the tyres, road surface, temperature and vertical load on each tyre. Worn tyres lose grip in wet and cold conditions before reaching 0.9 g. The effect of the squared speed should also not be forgotten. A ten per cent increase in speed leads to a twenty-one per cent increase in lateral G-values. This often surprises drivers.

Frequently asked questions

How is lateral acceleration calculated?

The lateral acceleration is calculated as a = v² divided by r, where v is the speed along the curve and r is the radius of curvature. This corresponds to the centripetal force in circular motion, directed towards the center of rotation. Dividing by 9.80665 gives an answer in g units. The equation can also be rearranged to solve for either velocity or radius.

What lateral acceleration values do typical passenger cars produce?

Typical passenger cars on dry roads with good tires usually have values between 0.7 and 0.9 g before the tires start to skid. High performance tires can achieve values over 1 g, and special race car tires routinely exceed this value. Formula One racing cars can reach values of over 5 g in fast corners due to aerodynamic downforce pushing the tires harder against the road surface.

Why does the g-value double when speed doubles?

In the formula, speed appears as v squared. So if you double your speed, that's a square of twice the value of v, which is four times what it was before. So lateral acceleration goes up by a factor of four. That explains why even a small increase in speed around a corner has such an out-sized effect and why a ten percent increase in speed leads to about a twenty-one percent increase in lateral G-force.

Does mass of an object affect lateral acceleration?

No. The lateral acceleration is determined only by the speed and radius. So a heavy truck and a light go-kart traveling at the same speed in the same curve will feel the same G-force. Only mass affects force. Centripetal force, which holds an object on a curved path, is the product of the object's mass and its acceleration (F = m a), so heavier objects need more force to stay on the same track.

What is the difference between lateral acceleration and centripetal acceleration?

From two perspectives, they are the same quantity. Centripetal acceleration is a term used in physics for the acceleration required to keep an object moving in a circular motion and it always acts inward. Lateral acceleration is a term used in everyday contexts, especially with vehicles, to refer to the same sideways force that occurs when turning corners. Both are equal to the square of the velocity divided by the radius, and both point toward the center of rotation.

What is the relationship between lateral acceleration and grip required for tires?

On a level road the lateral g-value is equivalent to the minimum required coefficient of friction for the tire. For curves that produce 0.85 lateral acceleration, at least a coefficient of friction of 0.85 is needed. If the lateral acceleration exceeds what the tires can provide, then the vehicle will skid. The banking of a curve reduces the grip required because it helps gravity pull the vehicle toward the center of the curve.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Centripetal force
Definition and derivation of centripetal acceleration and force for circular motion, including the v squared over r relation.
HyperPhysics: Centripetal acceleration
A concise reference on centripetal acceleration, the role of speed and radius, and the force that holds an object on a curve.
Wikipedia: Banked turn
How banking a curve lets a vehicle corner with less friction, and the ideal banking angle for a given speed and radius.