Prop diameter to hulll ratio
 

Just wondering,
Inboard boat. The center of the prop shaft (where the prop goes on at) is 9-1/2" from the keel of the hull. Is there a formula or rule on how big the diameter the prop should be for best results?

Biggest diameter you can fit is usually most efficient...usually.

General rule of thumb is a minimum tip to hull clearance of 15% of the diameter. 20% if you can get it.

With the 9.5" spacing you have, 16.5" diameter wheel would probably be the largest you can fit. 16.5"/2=8.25"...8.25"x1.15=9.49".

If you don't have a really good prop shop, I would recommend contacting Michigan Wheel, they have some smart folks with a lot of experience sizing (and engineering) propellers.

Without knowing the application- displacement, high speed planing, number of blades, skew, etc- it's hard to get more detailed.