I'm looking for a table showing which size of bar to use for a given volume to stir. Or a formula if there is one.
No chart I'm aware of. However, an informal and incomplete survey indicates most chemists to this by trial and error.
For pipe-type stir bars in flat bottom flasks/beakers, and you want a 'fast' stir, generally you want one roughly two thirds the size of your magnet arm to minimum the motor moving ahead of the magnet spin and 'flinging' it around. Obviously this is not possible if your flask is much smaller than the motor. If your stir bar is too close to the size of your vessel, you have 'catching' issues. with the sizes.
For egg-type stir bars in round bottom flasks, the concavity of the surface will help, but not eliminate 'flinging'.If you need a fast stir, you need a bigger stir bar. Personally, I've never needed larger than 3/4" because of my use preference, (also do not typically use roundbottoms larger than 1L).
Ultimately, however, remember stir bars are for mild to moderate stirring. If you need vigorous, you are better served with a mechanical stirrer. Additionally, if you are using very large (5L+) flasks, mechanical stirring is best.