The formula for converting revolutions per minute ( $rpm$ ) into radians per second ( $rad.s^{-1}$ ) is given by :

$$\omega = \frac{2\pi}{60} \times N$$

$$\omega_{ rad.s^{-1}} = \frac{2\pi}{60} \times N_{tr/min}$$

where :

• $N_{tr/min}$ is the angular velocity expressed in revolutions per minute [rpm]
• $\omega_{ rad.s^{-1}}$ is the angular velocity expressed in radians par seconde [rad/s]

Multiply the speed in revolutions per minute by $2\pi$ to obtain radians per minute.
Then divide the result by 60 to convert radians per minute to radians per second.

The following relationships can be deduced:

• 1 rad/s = 9.549296585513721 rpm
• 1 rpm = 0.10471975511965977 rad/s