Stopping distance under constant deceleration:
formula and worked example

What braking distance represents

Stopping distance under constant deceleration is how far an object travels from the moment braking begins until it is at rest. The word constant matters: the formula assumes the same braking rate throughout, which makes the maths clean and gives a solid first estimate for cars, bicycles, trolleys and trains.

The question it answers is practical. Given how fast something is moving and how hard it can brake, how much clear space does it need? Engineers use it for signal spacing and speed limits; drivers use it, often without noticing, whenever they judge a following gap.

The relationship and its two inputs

• Speed: the speed at the instant braking starts, in m/s. Divide km/h by 3.6, so 72 km/h becomes 20 m/s.
• Deceleration: the size of the braking rate, in m/s², entered as a positive number. A value of 5 means speed falls by 5 m/s each second.

The formula comes from rearranging v² = u² + 2as with the final speed set to zero. You do not need to know the stopping time to use it, which is why it is so convenient. If you want the time anyway, divide the speed by the deceleration.

Because the speed is squared, the units must be right before anything else. Feeding 72 instead of 20 gives a distance 13 times too large, an error that looks plausible until you compare it with the length of a football pitch.

Stopping from 20 m/s at 5 m/s²

1. 1Square the speed: 20 × 20 = 400.
2. 2Double the deceleration: 2 × 5 = 10.
3. 3Divide: 400 ÷ 10 = 40 m.
4. 4Cross-check with time: stopping takes 20 ÷ 5 = 4 s, and the average speed over that time is 10 m/s, so 10 × 4 = 40 m.

The cross-check is a good habit. The braking distance is simply the average speed during the stop (half the starting speed) multiplied by the time it takes.

Reading 40 m, and what it leaves out

Forty metres is about the length of a few cars nose to tail. That is the distance after the brakes bite. A real driver also travels during the reaction delay, at full speed, before braking even begins. Multiply the speed by the reaction time to estimate that extra distance: at 20 m/s, a one-second delay adds 20 m, so total stopping distance becomes 60 m.

The deceleration value is the weakest input in practice. On a surface with friction coefficient μ, the maximum braking deceleration is roughly μ times 9.81 m/s², so wet, icy or gravel surfaces produce much smaller values than dry tarmac. Brake condition, tyres and slope also move the number.

• Higher deceleration capability: shorter distance, but only if grip allows it.
• Downhill slope: effective deceleration falls and distance rises.
• Heavier load: does not change the ideal formula, but may stretch what the brakes can deliver.

How strongly speed drives the answer

A 10% rise in speed, from 20 to 22 m/s, raises braking distance from 40 m to 48.4 m, an increase of 21%. This is the squared term at work: 1.1 × 1.1 = 1.21.

Applied to a road, the effect explains why a modest overspeed removes much of a safety margin. At 5 m/s² the extra 8.4 m is about two car lengths, and an obstacle that a vehicle at 20 m/s would stop short of is hit at a noticeable speed by one doing 22 m/s.

Where braking calculations go wrong

• Using km/h directly in the formula, which inflates the result by a factor of about 13.
• Quoting the braking distance as the full stopping distance and forgetting reaction time.
• Entering deceleration as a negative number and getting a negative distance.
• Assuming the rate stays constant when the brakes fade, the surface changes, or an anti-lock system pulses.

Using it as a planning check

When checking a safe following gap, work backwards from the space available. Rearranging gives the maximum speed that still permits a stop within a given distance: speed equals the square root of 2 × deceleration × distance. For 40 m at 5 m/s², that returns 20 m/s, matching the example.

For safety-critical work, use a measured deceleration from a test or a conservative friction figure, never a convenient round number.