I have a circular overlay that can change according to the user's preferences: they have a circle of radius 'r' around them and a slider can change 'r' accordingly. So far it works perfectly well.

My problem is I don't know how to find the proper conversion from the circle's radius to the map's metric. As an example, given the circle below, what is the distance covered with the given radius?

![enter image description here](https://i.stack.imgur.com/ACtop.png)