Is There a Way to Find What Gears You Have?

FYI- I agree with just spinning it once. Pretty clear to see when the driveshaft spins 3 3/4 times (3.73)versus 3 1/2 times (3.55). Not that any other way is wrong.
 
With factory size tires and a T5 @ 60mph:

1682 rpm = 3.08's

1786 rpm = 3.27's

If the rear gears have been upgraded, but the speedo gear left stock, then guessing using the rpm vs speed will not work. Factor in the accuracy of the stock tach and it's even more of a guessing game. As others have mentioned, best way to tell is count tire revolutions vs. wheels revs.