erm, well the permutations of scale conversions must be mahoosive -you can find the likes in railway worlds but it doesn't always work for other reasons manufacturers choose to adopt.
Rule of thumb i.e. 1:12 to 1:16 -multiply by 12 then divide by 16 -orwhatever feaction of the two. At the end of the day if you have one dimension on a plan -be it in xx dims, convert it to mm/cm/metres then divide by the new scale.
I usually ignore the "scale" on a plan. I note the dimension off the plan in mm and multiply it by the converted figure to take me to my scale. A plan may be stated at 1:200 but when it's printed it may be different (I have lots of plans I've printed off on different sized paper to save cost). Thats about how simple I can think of it. So a plan in "3-56th of a foot to the inch! or some "illigitimate" scale originally on A0 blueprints prints out at 200mm long on A3 -so thats even more confusing -use the multiplier. If I know a length of something I scale it all of there -usually xxmm by y multiplier.
....how many scales do you want to convert between? If you wanted to there's thousands of permutations you could sit down and put on a spreadsheet if you fancy or you can just do one calc. and multiply everything by "x".
Rich