# Convert radians per second [rad/s] to meters per second [m/s] and vice-versa

## Online converter

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

m/s

## Explanation

Assume an object (or point) attached to a rotating wheel. The angular velocity of the wheel is defined by $$\omega$$ expressed in $$rad.s^{-1}$$. 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:

$$v=r\omega$$

and vice-versa:

$$\omega=\frac{v}{r}$$

If the previous demonstration did not convince you. You can extend the formula that convert angle to distance :

$$\alpha = \dfrac{L}{r}$$

by replacing

• the length $$L$$ by the linear velocity $$v$$
• the angle $$\alpha$$ by the angular velocity $$\omega$$