For an open carrier you can, put a chalk mark on one drum. Make the other drum stationary. Rotate the input shaft 10 times. Count how many times the free drum rotates- Say, it looks like about 8.2 times. The ratio will be approximately:
10 rotations of the input shaft times 2 divide by drum rotations
or,
10 x 2 / 8.2 = 2.44 ratio
If you want the answer to be more accurate, rotate the input shaft 20 times:
20 x 2 / 16.3 = 2.45 ratio
Rotate the input shaft as many times you want. Just multiply input shaft rotations x 2 and divide by the drum rotations to get the ratio.
[The reason you multiply by two is to account for the fact that one drum is stationary.]
Finally, you look up the ratios that were available from the factory and you'll easily see which one you've got.