Braking distance and stopping distance: formulas, examples and limits

The three learning formulas

Stopping involves two stages. First comes reaction distance: the distance travelled while you recognise the need to brake and react. Then comes braking distance: the distance travelled during braking until the vehicle stops. Add them to obtain stopping distance.

Use speed in kilometres per hour; these formulas give distances in metres:

• Reaction distance ≈ (speed ÷ 10) × 3
• Braking distance ≈ (speed ÷ 10) × (speed ÷ 10)
• Stopping distance = reaction distance + braking distance

At 50 km/h, the calculation is (50 ÷ 10) × 3 = 15 metres, then (50 ÷ 10)² = 25 metres. The estimated total is 15 + 25 = 40 metres. That is roughly the length of eight to ten parked cars, depending on their size.

Know the assumptions: this is a simplified learning model for ordinary braking, illustrated here for a dry, level road. The reaction formula corresponds to about 1.08 seconds. Your actual reaction time, grip, brakes, tyres, load and slope can produce very different results. The formula contains no guaranteed safety reserve and must not be used to choose a minimum distance in real traffic.

Table: reaction, braking and stopping distance from 30 to 120 km/h

Every number in this table is calculated with the same learning formulas. These are model values, not measurements of a particular car or road. Start with the 50 km/h example to understand how the two distances combine.

In this model, increasing speed from 30 to 120 km/h multiplies speed by four but stopping distance by ten, from 18 to 180 metres. Braking distance grows faster than reaction distance; do not multiply the entire stopping distance by the same factor.

Double the speed, four times the braking distance

With the same constant braking deceleration, braking distance is proportional to the square of speed. Doubling speed from 50 to 100 km/h changes the model's braking distance from 25 to 100 metres. Tripling speed multiplies that braking distance by nine.

The vehicle's kinetic energy also increases with speed squared. That energy must be dissipated during braking. Reaction distance behaves differently: with the same reaction time, doubling speed doubles reaction distance, from 15 to 30 metres in this example.

Even a small increase matters. At 60 km/h, the formulas give 18 metres of reaction distance plus 36 metres of braking distance: 54 metres rather than 40. Under exactly this constant-deceleration model and the same reaction time, the 60 km/h vehicle is still travelling at about 37 km/h where the 50 km/h vehicle has stopped. This worked comparison illustrates the effect of speed; it is not a prediction for every collision or braking system. A higher impact speed can make injuries more severe, particularly for unprotected pedestrians and cyclists.

What can increase braking distance?

Actual stopping performance depends on the conditions. Do not apply a fixed wet-road or winter multiplier to every vehicle.

Keep the two stages distinct: a change in tyre grip directly affects braking, not the arithmetic of reaction distance at an unchanged speed and reaction time. But poor visibility, difficult conditions or delayed recognition can also change when you react. Do not assume that the reaction stage is always unaffected. A lower speed reduces both distances under otherwise equal assumptions.

Emergency braking and ordinary braking

The ordinary-braking formula uses a lower deceleration than the emergency-braking learning formula used here. For the latter, divide the model's braking distance by two:

Emergency braking distance ≈ (speed ÷ 10)² ÷ 2. At 50 km/h, this gives 12.5 metres. Add the unchanged 15-metre reaction distance to obtain 27.5 metres. Only the braking part is halved; the whole stopping distance is not.

These are two teaching models. An actual emergency stop does not always halve a previously calculated braking distance. Braking technique depends on your vehicle; with ABS, firm sustained braking allows the system to limit wheel lock. ABS does not create extra grip or guarantee steering control on every surface. Learn the appropriate technique with an instructor in a suitable controlled setting.

Anticipation helps reduce the need for sudden braking, but an emergency can arise even when a driver has acted carefully. An emergency stop alone is not proof that the driver caused the danger. Keep sufficient distance and do not rely on ABS or a calculation to make up for excessive speed.

Being able to stop within the distance you can see

The essential Swiss rule is to choose a speed that allows you to stop within the distance you can see. Where it is difficult to pass an oncoming vehicle, the rule requires stopping within half that visible distance (VRV Article 4(1)). That is a condition you must satisfy; a posted speed limit is not permission to use that speed in every situation.

At night, do not assume that dipped headlights always provide exactly 50 metres of useful visibility. The lights, road alignment, weather and how easily an obstacle can be recognised all matter. For a worked example, if you can see only 50 metres clearly, the model's 88-metre stopping distance at 80 km/h does not fit. This example explains the problem; it does not set a universal safe night-time speed.

Apply the same reasoning in fog, heavy rain and blind bends. Slow down to suit what you can actually see and the available grip. Read dipped and main-beam headlights for the lighting rules, and Swiss speed limits for the maximum speeds that apply to different roads and vehicles.

For a learning check, choose a speed, work out both distances and add them. Then ask which assumptions could change in real traffic. The free English theory quiz is an existing next step for practice; it currently opens the general quiz.