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# Convert revolutions per second [rps] to meters per second [m/s] and vice-versa

## Online converter

Convert any value from / to revolutions per second [rps] to meters per second [m/s], angular velocity to linear velocity. Fill one of the following fields, values will be converted and updated automatically.

rps
m/s

## Explanation

Assume an object (or point) attached to a rotating wheel. The angular velocity of the wheel is defined by $$N$$ expressed in $$rps$$. The angular velocity of the wheel can be converted to $$rad.s^{-1}$$ thanks to the following formula:

$$\omega_{ (rad.s^{-1}) } = 2\pi.N_{(rps)}$$

This also means that the wheel rotates from $$\omega$$ radians during one second. During that same second, the attached object (or point) travels a distance of $$r \times \omega$$. It implies that the speed of the object is also equal to $$r \times \omega$$. The conversion can be done thanks to the following formula:

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

and vice-versa:

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