Could you explain the process to convert rpm to km/h?

To explain the process to convert an angular velocity expressed in rpm into a linear velocity expressed in km/h, let's consider the following vehicle:

• The radius of the wheels is  , expressed in meters [m].
• The angular velocity of the wheels is  expressed in revolution per minute [rpm].
• The linear velocity of the vehicle is , expressed in kilometres per hour [km/h].

Step 1. Convert angular velocity to rad/s.

Angular velocity N represents the number of turn during one minute. To get the number of revolution in one second, we just have to divide  by 60. Since, one revolution is equal to  radians, we can deduce the angular velocity expressed in rad/s:



Step 2. Convert angular velocity to linear velocity

The formula to convert linear velocity to angular velocity is given by , in our case, the result is expressed in m/s:



By merging step 1 and 2, we get:



Step 3. Convert linear velocity from m/s to km/h.

To convert m/s to kilometres per hour, we need two arithmetic operations :

• convert seconds to hours (multiply m/s by 3600)
• convert meters to kilometers (divide by 1000)

The formula to convert meters per second to kilometres per hour is given by :



By merging step 1, 2 and 3, we finally get :



The last equation can be simplified:





We get the final formula from rpm to km/h:



Since the diameter of the wheels is twice the radius of the wheels, the last formula can also be expressed as :



To explain the process to convert an angular velocity expressed in rpm into a linear velocity expressed in km/h, let's consider the following vehicle:

• The diameter of the wheels is  , expressed in meters [m].
• The angular velocity of the wheels is  expressed in revolution per minute [rpm].
• The linear velocity of the vehicle is , expressed in kilometres per hour [km/h].

Step 1. Convert angular velocity to rad/s.

Angular velocity N represents the number of turn during one minute. To get the number of revolution in one second, we just have to divide  by 60. Since, one revolution is equal to  radians, we can deduce the angular velocity expressed in rad/s:



Step 2. Convert angular velocity to linear velocity

The formula to convert linear velocity to angular velocity is given by , in our case, the result is expressed in m/s:



By merging step 1 and 2, we get:



Step 3. Convert linear velocity from m/s to km/h.