And now that everyone has explained it throw it all away and learn how to use tool comp. Don't waste months and months like I did because I had the idea tool comp is complicated. On a mill it is trivial, on a lathe a bit more involved because you need to take into account the tool vector direction but in all cases it is a heck of a lot simpler than doing the tedious calculations for manual compensation in a hand written program.
Also when you do it by hand you are stuck with using that tool diameter; with tool comp you can change tool diameter and compensate for undersize or oversize tools.
An open mind is a virtue...so long as all the common sense has not leaked out.