Difference between view speed and distance horizontal

When I try converting my sensitivity from a FPS game with a 360 distance of 12 inches to a game like OSU where it is only the screen I am confused on how to get true 1 to 1. More specifically what is the difference between the view speed and the distance horizontal for converting the sensitivity. On another note is there a place I can find a full guide on how to use the sensitivity converter to it's full capability? 

Thanks for the help in advance. I look forward to hearing more about my issue.