## Introduction

You can't actually convert radians to millimeters. Radian is a measure of angle, while meters is a unit of distance. There is an homogeneity issue between the two quantities.

## Online converter

Convert any value from / to radians [rad] to millimeters [mm], angle to length. Fill one of the following fields, values will be converted and updated automatically. Note that the radius is expressed in meters.

mm

## Explanation

As explained above, you can't actually convert millimeters to radians. Radian is a measure of angle, while millimeters is a unit of distance. There is an homogeneity issue between the two quantities.

However, there are many mechanical systems that transform linear motion into rotary motion. The most obvious system is the wheel: the rotation of the wheel moves the vehicle forward and vice versa. These systems can be reduced to the calculation the length of the arc of a given angle on a circle of radius $$r$$. In this case, the formula governing such a system and allowing to transform a displacement (of the vehicle) given in meters into a rotation (of the wheels) of an angle expressed in radians is given by:

$$L = 1000 \times r \times \alpha$$

and vice-versa:

$$\alpha=\frac{L}{1000 \times r}$$

with :

• $$L$$ the distance or length expressed in millimetres [mm]
• $$r$$ is the radius expressed in metres [m]
• $$\alpha$$ is the rotation angle expressed in radians [rad]