Convert revolutions per minute [rpm] to kilometers per hour [km/h] with gear ratio 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 with gear ratio. Fill one of the following fields, values will be converted and updated automatically.
Formulas
Explanation
First let's consider the gear ratio. The ratio divides the input angular velocity according to the following formula:
$$ N^{output}_{(rpm)}= \dfrac { N^{input}_{(rpm)}}{ratio} $$
The angular velocity of the wheel (in rpm) can be converted into \( m.s^{-1} \) thanks to the following formula:
$$ v_{(m.s^{-1})} = r \times \omega_{(rad.s^{-1})} = r \times \frac {2 \pi }{60.ratio}.N^{input}_{(rpm)} $$
It becomes easy to convert this linear velocity expressed in \(m.s^{-1} \) into \(km.h^{-1} \) thanks to the following formula:
$$ v_{ (km.h^{-1}) } = \frac {3600}{1000}.v_{(m.s^{-1})} = \dfrac{3.6}{ratio} \times v_{(m.s^{-1})}$$
By merging the two previous equations, we can deduce the relationship between revolution per minute [rpm] and kilometers per hour [km/h]:
$$ v_{ (km.h^{-1}) } = \frac {3600}{1000} \times r \times \frac {2 \pi }{60.ratio}.N_{(rpm)} = \frac {3}{25.ratio}. \pi. r . N^{input}_{(rpm)} $$
et vice versa:
$$ N^{input}_{(rpm)} = \frac {25.ratio} { 3. \pi . r} v_{(km.h^{-1})} $$
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