How can I find a Formula to figure out

the difference in the distance of the in

side and outside of a dog racing track?

We can assume the track is a circle.

Because, if it is really rectangle with a half circle at each end, the inside and outside distances along the straight sides are the same.

So, if you know the inside diameter of the track, d, and the width of the track, w, then the outside diameter D = d+2w.

2πD - 2πd is the difference in distances.