Re: diagnosing a gear ratio
The easiest way is to read it from the sticker.

. You may be able to use the serial number to determine it too assuming someone didn't rebuild it and change it.
Barring that you can count teeth on the gears if it's apart or if removed, put it in gear, turn the drive shaft 10-20 turns or so, and have someone count the turns of the prop (you may need a protractor to measure fractions of a turn if you REALLY want to be accurate) and get out the calculator.
input shaft turns divided by propshaft turns = ratio (Yoke/Prop=ratio)
If it's a 1.5:1 or 2:1 drive it's easy.....3 turns of the yoke will produce 2 prop turns or 2 turns to 1 turn respectively.
If it's 1.43 to 1 you'll have to turn the input shaft more turns.... 143 to be precise. it would be 143 revs of the yoke to 100 revs of the prop etc.... This is where the protractor comes in handy...
For example, with a 1.43:1 drive the input shaft (engine) turns 1.43 revolutions for every 1 revolution of the prop......... If you measure exactly 1 turn of the prop. you would have to measure 1.43 "turns" of the yoke....... 0.43 times 360 degrees would be about 155 degrees.
so 1.43 turns would be 1 revolution + 155 degrees more