Got a set of 255/45/18's in the rear so when I went to recalibrate my speedo it asked me that! I can get the manufacturers overall diameter but what's the formula for the calculation?
Use a tape measure or other measuring device and determine the tire circumference. You might be able to get this value off Tire Rack's website and not have to measure it.
Convert this value to Feet.
1 mile = 5280 Feet
Divide 5280 Feet by the circumference you measured above (in feet).
The resulting value is the number of tire revolutions per mile.
Most tire manufacturers give the specs for revs/mile, and tire rack has that info too.
If you do know the diameter though, it is 5280/(Pi*d/12), where d = diameter in inches.
Interestingly enough, the revs per mile changes as the tire gets older and more worn out since the diameter is changing. I wonder if the manufacturer specs use the "new" tire life or an average. Either way, it doesn't throw off your odometer / speedometer much in the long run.