What is stopping distance, and how do you calculate it?

Imagine a ball rolls into the road in front of a car. The car does not stop at the instant the driver sees it. First the driver has to notice the ball, decide to brake and move a foot to the pedal. During that time the car keeps going at full speed. Then the brakes go on, and the car still slides forward while it slows down. Physics splits the stopping distance into these two parts:

stopping distance = thinking distance + braking distance

The thinking distance (also called reaction distance) is how far the car travels during the driver's reaction time. The car is moving at a steady speed, so you use the same idea as in speed, distance and time:

thinking distance (m) = speed (m/s) × reaction time (s)

A typical reaction time is around 0.7 seconds, but it can easily be more than a second. At 20 m/s (about 45 mph or 72 km/h) a reaction time of 0.7 s gives a thinking distance of 20 × 0.7 = 14 m, before the car has even started to slow down.

The braking distance is how far the car travels once the brakes are on. The brakes use friction to do work against the car's motion until all its kinetic energy is gone. Work done = force × distance, and kinetic energy = ½mv², so:

braking force × braking distance = ½ × mass × speed²

Rearranged with deceleration a (in m/s²), this gives braking distance = v² ÷ (2a). The key thing to notice is the square. If the speed doubles, the thinking distance doubles, but the braking distance becomes four times as long. At high speed the braking distance is by far the bigger part.

What changes each part?

• Thinking distance gets longer with higher speed, and with anything that slows reactions: tiredness, distractions such as a phone, and alcohol or drugs.
• Braking distance gets longer with higher speed, a heavier vehicle (more mass to stop), worn brakes or tyres, and a slippery road: wet, icy, oily or covered in leaves or gravel. The UK Highway Code says stopping distances are at least double on wet roads and can be ten times longer on ice.

This is also why speed matters so much in a crash. The momentum and the kinetic energy that must be removed both grow with speed, and kinetic energy grows with speed squared, so a car at twice the speed carries four times the energy into a collision.

What is the formula for stopping distance?#

Stopping distance = thinking distance + braking distance. Thinking distance = speed × reaction time, and braking distance = v² ÷ (2a), where a is the deceleration. In kinematics you get the same result from v² = u² + 2as (on the GCSE equation sheet as v² − u² = 2as): with final speed v = 0 and a the size of the deceleration, s = u² ÷ (2a).

What does stopping distance depend on?#

On speed (the biggest factor), on the driver (reaction time: tiredness, distractions, alcohol and drugs) and on the vehicle and road (brakes, tyres, mass, and whether the road is dry, wet or icy).

What is the stopping distance at 30 mph and at 70 mph?#

The UK Highway Code gives typical values for a car on a dry road of 23 m at 30 mph (9 m thinking + 14 m braking) and 96 m at 70 mph (21 m thinking + 75 m braking). These are averages; real distances can be longer.

How do you remember stopping distances?#

One popular trick works in feet: multiply the speed in mph by 2 at 20 mph, 2.5 at 30 mph, 3 at 40 mph, and so on up by 0.5 each time. That gives 40 ft, 75 ft, 120 ft, 175 ft, 240 ft and 315 ft, which match the Highway Code distances in metres (12 m to 96 m). For thinking distance alone, it is 3 m for every 10 mph.

What is the stopping distance in rain or ice?#

On a wet road the Highway Code says stopping distances are at least double, and on ice they can be ten times longer, because the tyres have much less grip. The thinking distance does not change; the braking distance does.

Why does a train or a ship need so far to stop?#

A train has a huge mass and steel wheels on steel rails give little friction, so it can need hundreds of metres or more. A large ship has an enormous mass and only the water to slow it, so it can take several kilometres.

What is a safe following distance?#

The Highway Code advises leaving at least a two-second gap behind the vehicle in front on fast roads, and at least double that in the wet. At 20 m/s, two seconds is 40 m.