# Formula to calculate Braking Distance

How do we calculate Braking distance? This distance refers to the distance a vehicle will travel from the point where its brakes are fully applied to when it comes to a complete stop. It is affected by the following:

• the original speed of the vehicle
• the type of brake system in use
• the reaction time of the driver/rider and
• the coefficient of friction between its tires and the road surface.

The theoretical braking distance can be found by determining the work required to dissipate the vehicle’s kinetic energy.

The kinetic energy E is given by the formula:

E = (1/2)mv2,

where m is the vehicle’s mass and v is its speed.

The work W done by braking is given by:

W = μmgd,

where μ is the coefficient of friction between the road surface and the tires, g is the gravity of Earth, and d is the distance travelled.

The braking distance (which is commonly measured as the skid length) given an initial driving speed v is then found by putting W = E, from which it follows that

d = v2/(2μg).

The maximum speed given an available braking distance d is given by:

v = √(2μgd).

Note that these theoretical formulas do not take account of the driver’s reaction time (an example is a two-second rule).