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Exact drive ratios of bicycle hub gears
Brand Speeds Model[1] Shifter position
-4 -3 -2 -1 (near) unity +1 +2 +3 +4
Ratio
Bendix 2-speeds Red Band, Yellow Band         15/22 1        
Blue Band         1 1   7/15      
3-speeds (See Sachs, SRAM)         47/64 1 1  17/47      
Rohloff Speedhub, 14-speed Each value in this row is the one directly below it, times the third-stage ratio of 221/541. 3315[2] 5304[3] 34255[4]  221/541 38896[5] 6851[6] 4862[7]  
11902[8] 16771[9] 95216[10] 83855[11] 12984[12] 8115[13]
For these ratios, the third stage is locked at unity.   15/22   24/31  155/176 1 1  21/155 1   7/24 1   7/15  
Sachs, SRAM 2-speeds Doppel-torpedo         16/21 1        
Automatic, Duomatic         1 1  17/47      
Orbit         48/65 1        
3-speeds 25,29        3/5     3/4  1        
Universal Dreigang          4/5  1 1   1/4       
53          3/4  1 1   1/3       
55          3/4  1 1   1/3       
All 3-speeds 1970-, DualDrive         47/64 1 1  17/47      
4-speed Universal Torpedo        3/5     3/4  1 1   1/3       
5-speeds Sachs H 5100, 5113, 5120, 5213        2/3     7/9  1 1   2/7  1   1/2     
SRAM P5 5-speeds       19/30   57/73 1 1  16/57 1  11/19    
7-speeds Sachs Torpedo H 7203, -13, -20    273/460   21/31   75/92 1 1  17/75 1  10/21 1 187/273  
Sachs Super 7, SRAM S7, MH7205, -15, -25  252/439   21/31   72/89 1 1  17/72 1  10/21 1 187/252  
9-speed SRAM I-Motion 9[14]   13/24   18/29    8/11   64/75 1 1  11/64 1   3/8  1  11/18 1  11/13 [15]
12-speed Sachs Elan 12-speed Speeds 1 through 6: ? ? 1[16] ? ? ?  
Speeds 7 through 12: ? ? ? ? ? ?  
Shimano 3-speeds 333, SG-3S21, G-3S23, F, G, 3SC, 3CC          3/4  1 1   1/3       
Nexus Inter 3         11/15 1 1   4/11      
4-speed Nexus Inter 4         1 1  19/78 1   1/2  1 285/338  
7-speeds Nexus 7-speed     12/19   20/27 3348[17]  620/627[18] 1  43/297 1  70/209 1   6/11  
3971[19]
8-speeds Nexus, Alfine 8-speed   49/93 [20] 22589[21] 8194[22]  343/403[23] 1 1  84/377 1  49/117 1   8/13  
35061[24] 10881[25]
Sturmey-Archer (Also licensees and copies: Brampton, Hercules, NK, Schwinn-Approved, Sears, Styre, SunTour for the AW, BSA for the X.) 2-speeds S2          5/7  1        
T,TB,TBC,TBF,TBFC,TF          3/4  1        
TC close-ratio fixed         45/52 1        
3-speeds Original 1902          4/5  1 1   1/4       
A, C, F, FN, FX, N, S, V, X, BSA         16/21 1 1   5/16      
AB, AB3, AG, AT, AT3, AW, AW3, AWC, C30, K, KB, KC, KT, KTC, QS-RC3, RD-RB3, RS-RF3, RS-RR3, RX-RD3, S30, S3B, S3C, SAB3, SBR, S-RB3, S-RC3, S-RF3, SX-RB3, SX-RK3, TCW, TS-RC3, TS-RF3, XL-RD3, X-RD3          3/4  1 1   1/3       
AC         12/13 1 1   1/15      
AF, ASC fixed        3/4     9/10 1        
AM, AM Tandem         45/52 1 1   7/45      
AR         69/74 1 1   5/69      
KS          8/9  1 1   1/8       
KSW          6/7  1 1   1/6       
S3X     5/8 3/4 1        
SW         13/18 1 1   5/13      
4-speeds FB, FG, FW        2/3    15/19 1 1   4/15      
FC        3/4     9/10 1 1   1/11      
FM        2/3     6/7  1 1   1/8       
5-speeds AB5, AT5, S5, S5/1, S5/2, S5C, 5-Speed Alloy, 5 Star, Sprinter 5, XRD5, XRF5         2/3    15/19 1 1   4/15 1   1/2     
S50(W), S5C(W), S5S(W), S-RC5(W), S-RF5(W), XL-RD5(W), X-RC5(W), X-RD5(W), X-RF5(W)        5/8     3/4  1        1   1/3  1 3/5    
7-speeds AT7, S7, S7C, X-RD7, Sprinter 7[26]      3/5    20/29  115/143 1 1  28/115 1   9/20 1   2/3   
8-speeds X-RD8, X-RF8, X-RK8, X-RR8[27] This hub only gears up.  Gears 1 through 4: 1 1   9/32 1   9/20 1  47/73  
Gears 5 through 8: 1 549/640 2  31/292 2  28/73 3 63/1168[28]  
S80(W), X-RD8(W), X-RF8(W), X-RK8(W) This hub only gears up.  Gears 1 through 4:   1[29] ? ? ?  
Gears 5 through 8:   ? ? ? ?  
[1]
John Allen:
Lines in pink: need verification. Lines in blue: insufficient information or no information.
[2]
John Allen:
Numerator entered as an integer
[3]
John Allen:
Numerator entered as an integer
[4]
John Allen:
Numerator entered as an integer
[5]
John Allen:
Numerator entered as an integer
[6]
John Allen:
Numerator entered as an integer
[7]
John Allen:
Numerator entered as an integer
[8]
John Allen:
Denominator entered as an integer.
[9]
John Allen:
Denominator entered as an integer.
[10]
John Allen:
Denominator entered as an integer.
[11]
John Allen:
Denominator entered as an integer.
[12]
John Allen:
Denominator entered as an integer.
[13]
John Allen:
Denominator entered as an integer.
[14]
John Allen:
Reverse-engineered.
[15]
John Allen:
SRAM literature says 1.844 but calculation says 1.846.
[16]
John Allen:
This is unity ratio. Manufacturer only give other ratios to 2 decmial places.
[17]
John Allen:
Numerator entered as an integer
[18]
John Allen:
Ratio is achieved by gearing down, then up.
[19]
John Allen:
Denominator entered as an integer
[20]
John Allen:
This ratio is that of the fifth speed, times the first-stage ratio of 49/93.
[21]
John Allen:
Numerator entered as an integer. Ratio is that of the 6th speed times the first-stage ratio of 49/93.
[22]
John Allen:
Numerator entered as an integer. Ratio is that of the 7th speed, times the first-stage ratio of 49/93.
[23]
John Allen:
Ratio is that of the 8th speed times the first-stage ratio of 49/93.
[24]
John Allen:
Denominator entered as an integer. Ratio is that of the 6th speed times the first-stage ratio of 49/93.
[25]
John Allen:
Denominator entered as an integer. Ratio is that of the 7th speed times the first-stage ratio of 49/93.
[26]
John Allen:
Ratios are almost certainly correct, reverse engineered.
[27]
John Allen:
Ratios are derived from tooth counts in Sturmey-Archer technical information.
[28]
John Allen:
Number inserted as text; Excel will not generate fraction with 4-digit denominator.
[29]
John Allen:
Fractional ratios are unavailable. This is the only one which can be determined exactly.