What this calculator does
Acceleration is how quickly speed changes, and the same arithmetic run backwards gives braking. The part people underestimate is that braking distance depends on the square of speed, so it grows far faster than the speed does.
The other half of stopping is reaction time, during which the vehicle is still travelling at full speed. At 100 km/h a vehicle covers about 28 metres every second, so a one second reaction adds 28 metres before the brakes have done anything at all.
The formula
Acceleration is the change in speed divided by the time taken, with speeds converted to metres per second. Braking distance is speed squared divided by twice the friction coefficient times gravity. Total stopping distance adds the distance covered during the reaction time.
| Term | Meaning |
|---|---|
| Friction coefficient (μ) | How much grip there is between tyre and road. Dry sealed road is often around 0.7, wet noticeably less, ice far less. |
| Reaction time | The delay between seeing a hazard and the brakes taking effect. Often taken as about one second for an alert driver. |
| g | One g is the acceleration of gravity, 9.81 m/s². Braking at 0.7 g is firm but within the grip of a dry road. |
The inputs explained
| Field | What to enter |
|---|---|
| Initial speed (km/h) | The starting speed in kilometres per hour. Use zero for accelerating from rest. |
| Final speed (km/h) | The final speed in kilometres per hour. This is also the speed used for the braking distance figures. |
| Time taken (s) | The time taken for the change in speed, in seconds. |
| Braking friction coefficient | The friction coefficient between tyre and road. Lower it substantially for wet or loose surfaces. |
| Reaction time (s) | The reaction time in seconds, used only for the total stopping distance. |
When to use it
Comparing stopping distances between speeds
The jump in braking distance between two speeds is much larger than the difference in speed suggests, and this makes the size of it concrete.
Allowing for a wet road
Reducing the friction coefficient shows how much further a vehicle travels before stopping on a surface with less grip.
Checking an acceleration figure
A quoted zero to one hundred time converts directly into an average acceleration in m/s² and in g.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does stopping distance change with speed?
The same vehicle and road surface at two different speeds.
| Speed | Braking distance | Total stopping distance |
|---|---|---|
| 50 km/h | 14.1 m | 27.9 m (incl. reaction) |
| 100 km/h | 56.2 m | 84.0 m (incl. reaction) |
Questions
Why does braking distance quadruple when speed doubles?
Because the brakes have to remove kinetic energy, and that energy depends on the square of speed. Twice the speed means four times the energy, and at a given braking force that takes four times the distance.
What friction coefficient should I use?
Around 0.7 is a common figure for a dry sealed road with decent tyres. Wet roads are lower, and loose gravel or ice lower still. The figure varies with tyre, surface and temperature, so treat any single value as an estimate.
Is reaction time really a full second?
About a second is a common planning figure for an alert driver who is already watching the hazard. It is longer when tired, distracted or surprised, and it is the part of stopping distance that no amount of braking performance can shorten.
Does a heavier vehicle take longer to stop?
In this simplified model, no: mass cancels out, because a heavier vehicle has more kinetic energy but also presses the tyres down harder. In reality heavier vehicles do stop less well, because brakes fade with heat and tyre grip does not rise quite in proportion to load.
For the energy behind the braking, see the kinetic and potential energy calculator. For the grip figure itself, see the friction force calculator.