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Shimano 7-speed[1]
  Number of gear teeth       Number of gear teeth            
Gear Sun Gear  1 Pinion to Sun 1 Pinion to Ring 1 Ring gear 1 Path: 1=R to P, 2=Direct, 3=P to R Gear Drive Ratio Stage 1 drive ratio as fraction Sun Gear 2 Pinion to Sun 2 Pinion to Ring 2 Ring gear 2 1=R to P, P to S 2=Direct, 3=P to R   Stage 2 drive ratio Stage 2 drive ratio as fraction Total Drive Ratio[2] Total drive ratio as fraction Ratio incre- ment
1 42 14 14 72 1 0.632    12/19   30 19 14 66 2 1.000 1           0.632    12/19    
2 36 20 14 72 1 0.741    20/27   30 19 14 66 2 1.000 1           0.741    20/27   1.173
3 42 14 14 72 1 0.632    12/19   30 19 14 66 3 1.335 1   70/209  0.843  3348/3971 [3] 1.138
4 36 20 14 72 1 0.741    20/27   30 19 14 66 3 1.335 1   70/209  0.989[4]   620/627  1.173
5 36 20 14 72 1 0.741    20/27   36 14 14 66 3 1.545 1    6/11   1.145 1   43/297  1.158
6 36 20 14 72 2 1.000 1           30 19 14 66 3 1.335 1   70/209  1.335 1   70/209  1.166
7 36 20 14 72 2 1.000 1           36 14 14 66 3 1.545 1    6/11   1.545 1    6/11   1.158
[1]
John Allen:
Teeth counted by Konstantin Shemyak.
The disassembly/reassembly instructions for the hub, at www.shimano.com/publish/content/global_cycle/en/us/index/tech_support/tech_tips.download.-Par50lparsys-0022-downloadFile.html include detailed photos and drawings.
[2]
This ratio is the product of those of the first and second stages
[3]
John Allen:
Oddly, Excel gives a 4-digit numerator and denominator.
[4]
John Allen:
A direct-drive unity ratio would be possible in theory, by driving from the first stage and disengaging the second stage..However, it could lead to rough shifting.