The formula for converting an angular velocity expressed in radians par secondes ( $rad.s^{-1}$ ) into a linear velocity expressed in meters per seconds ( $m.s^{-1}$ ) is given by :

$$v = r \times \omega$$

With :

• $\omega$ : angular velocity expressed in $rad.s^{-1}$
• $v$ : linear velocity expressed in $m.s^{-1}$
• $r$ : radius, expressed in $m$

There is an online converter which directly converts angular velocity into linear velocity.

Example

For example, if a vehicle with wheels of radius 10 cm rotates at 20 rad/s, the vehicle speed is given by :

$$v = r \times \omega = 0.1 \times 20 = 2~ m.s^{-1}$$