# Please explain process to convert rpm in to kmph

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

**Step 2.** Convert angular velocity to linear velocity

The formula to convert linear velocity to angular velocity is given by

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 :