# Convert degrees [°] to meters [m] and vice-versa

## Introduction

You can't actually convert degrees to meters. Degrees 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 degrees [°] to meters [m], angle to length. Fill one of the following fields, values will be converted and updated automatically.

°
m

## Explanation

As explained above, you can't actually convert meters to degrees. Degrees is a measure of angle, while meters 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:

$$L = r * \alpha$$

By converting the angle from radians to degrees, it becomes easy to get the formula for converting meters to degrees:

$$\alpha_{ (rad) } = \frac {\pi \times \alpha_{ (deg) } } {180}$$

The equation from converting degrees to meters becomes:

$$L_{(m)} = \frac {r \times \pi \times \alpha_{ (deg) } } {180}$$

and vice-versa:

$$\alpha_{ (deg) } = \frac {180 \times L_{(m)} } {r \times \pi}$$

with :

• $$L$$ the distance or length expressed in metres [m]
• $$r$$ is the radius expressed in metres [m]
• $$\alpha$$ is the rotation angle expressed in degrees [deg] or [°]