What the inputs mean
- Speed: the speed when the need to stop appears.
- Reaction time: the time between seeing the need to stop and the brakes starting to act. The car keeps its full speed during it. The default of 1.5 s is an example value, not a rule.
- Friction coefficient: how hard the tires can grip the road, written as μ (mu). The deceleration is μ times gravity on level ground, so 0.7 means 0.7 g. It is an assumption: a dry road, a wet road, gravel or snow give very different values, and so do the tires and the brakes.
- Grade: the road's slope in percent, rise over run. Uphill shortens the braking distance, downhill lengthens it.
The formulas
stopping distance = reaction distance + braking distancereaction distance = v × t braking distance = v² ÷ (2 × μ × g)on a grade: braking distance = v² ÷ (2 × g × (μ cos a ± sin a)), a = atan(grade % ÷ 100)v is the speed in meters per second, t the reaction time and g = 9.80665 m/s², standard gravity. Use + uphill and − downhill. The model assumes the deceleration stays constant from the moment the brakes act until the car stops.
Worked example
60 mph is exactly 26.8224 m/s. With a 1.5 s reaction time, the car covers 26.8224 × 1.5 = 40.23 m, or 132 ft, before braking. With μ = 0.7, the braking distance is 26.8224² ÷ (2 × 0.7 × 9.80665) = 52.40 m, or 172 ft. The total is 92.64 m, or 304 ft, and the car stops 5.4 s after the need appears. The reaction share is 43% of the total.
On a 6% downhill grade with the same inputs, the braking distance grows to 57.42 m (188 ft) and the total to 97.65 m (320 ft). At 100 km/h on level ground, the total is 97.9 m.
Why speed matters so much
Reaction distance grows in step with speed, but braking distance grows with the square of speed. Doubling from 30 to 60 mph doubles the reaction distance, from 66 to 132 ft, and multiplies the braking distance by four, from 43 to 172 ft, with the example values. The table shows this across speeds. These are physics estimates; real stops depend on the car, the tires, the brakes, the road and the driver.
Questions
How do you calculate braking distance?
Divide the speed squared by 2 × μ × g, with the speed in m/s and g = 9.80665 m/s². At 60 mph (26.8224 m/s) and μ = 0.7, that is 52.40 m, or 172 ft.
What is the stopping distance at 60 mph?
With a 1.5 s reaction time and a friction coefficient of 0.7, both example values, it is 132 ft of reaction distance plus 172 ft of braking, 304 ft in total. Different values give different results.
What is the difference between braking distance and stopping distance?
Braking distance counts only from when the brakes act. Stopping distance adds the reaction distance before that. At 60 mph with 1.5 s, the reaction part alone is 132 ft.
How does a downhill grade change braking distance?
Gravity pulls the car down the slope, so less of the grip goes into slowing it. At 60 mph with μ = 0.7, a 6% downhill grade raises the braking distance from 172 ft to 188 ft.