How to use the stopping distance calculator
- Choose the units: miles per hour and feet, or kilometers per hour and meters.
- Enter the speed, the reaction time in seconds and the tire-road friction.
- Enter the road grade in percent. Use a positive number for uphill and a negative one for downhill.
- Read the reaction, braking and total distances, and the table for other speeds under the same conditions.
Formula
reaction distance = speed x reaction time
slowing rate a = g x (friction x cos(angle) + sin(angle)), with g = 9.80665 m/s squared
braking distance = speed squared / (2 x a)
time to stop = reaction time + speed / a
The angle comes from the grade: tan(angle) = grade / 100. A downhill grade makes the sine term negative, so the vehicle slows less and needs more room.
Sixty miles an hour on dry and wet roads
At 60 mph (26.82 m/s) with a reaction time of 1.5 seconds, the car covers 132 feet before the brakes are pressed. With a friction value of 0.7, the slowing rate is 6.86 m/s squared and braking takes 171.9 feet, so the total is 303.9 feet and the stop takes 5.41 seconds.
With a friction value of 0.4, an example for a wet road, braking takes 300.9 feet and the total is 432.9 feet. On a 6 percent downhill grade with a friction of 0.7 the total is 320.4 feet. At 50 km/h with a friction of 0.15, an example for ice, the total is 86.4 meters. The table lists 20 to 80 mph in the same conditions.
Why speed matters so much
Reaction distance grows in step with speed, but braking distance grows with the square of speed. Doubling the speed makes braking distance four times as long. That is why the table jumps from 19 feet of braking at 20 mph to 306 feet at 80 mph. The reaction time is a human factor and varies with attention, age and distractions, so treat the default as an example, not a rule.
Friction depends on the tire, the road surface and its condition. The values here are rough examples, not measured numbers, and real surfaces can change from one meter to the next.
Limits of the model
The model assumes the vehicle slows at a constant rate from the moment the brakes are applied. It does not include brake fade, anti-lock systems, load, tire wear, wind or the time the brakes take to build force. Real stopping distances can be longer, so leave far more room on the road than the table shows. For other motion problems, see the Kinematics Calculator, to check a speedometer, the Speedometer Error Calculator, and to compare tire sizes, the Tire Size Calculator.
Assumptions and limits
- The vehicle slows at a constant rate once the brakes are applied.
- The road grade is the slope along the direction of travel.
- Friction is one number for the whole stop.
- The speed, reaction time and friction shown when the page opens are examples.
- This is a learning tool and not a safety rating.
Frequently asked questions
What is a reasonable reaction time?
Studies of drivers report a wide range, and the figure depends on the driver and the situation. The page starts with 1.5 seconds as an example you can change.
What friction value should I use?
There is no single answer. Dry pavement is often modeled near 0.7, wet pavement lower, and ice much lower. The examples on this page are rough and are not measurements of any road.
Why can a downhill road make the stop impossible?
If the friction is lower than the slope, gravity pulls the vehicle forward as strongly as the brakes hold it back. The page then says the vehicle cannot slow down on that grade.
Does the page include the time to press the brake pedal?
That small time is part of the reaction time you enter. The model then assumes full braking from the moment the brakes act.