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# Convert revolutions per minute [rpm] to kilometers per hour [km/h] and vice-versa

## Online converter

Convert any value from / to revolutions per minute [rpm] to kilometers per hour [km/h], angular velocity to linear velocity. Fill one of the following fields, values will be converted and updated automatically.

rpm
km/h

## Explanation

The angular velocity of the wheel (in rpm) can be converted into $$m.s^{-1}$$ thanks to the following formula :

$$v_{(m.s^{-1})} = r \times \omega_{(rad.s^{-1})} = r \times \frac {2 \pi }{60}.N_{(rpm)}$$

It becomes easy to convert this linear velocity expressed in $$m.s^{-1}$$ into $$km.h^{-1}$$ thanks to the following formula :

$$v_{ (km.h^{-1}) } = \frac {3600}{1000}.v_{(m.s^{-1})} = 3.6 \times v_{(m.s^{-1})}$$

By merging the two previous equations, we can deduce the relationship between revolution per minute [rpm] and kilomèters per hour [km/h] :

$$v_{ (km.h^{-1}) } = \frac {3600}{1000} \times r \times \frac {2 \pi }{60}.N_{(rpm)} = \frac {3}{25}. \pi. r . N_{(rpm)}$$

et vice versa:

$$N_{(rpm)} = \frac {25} { 3. \pi . r} v_{(km.h^{-1})}$$