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Gain Ratios--
A New Way to Designate Bicycle Gears

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by Sheldon "Quixote" Brown
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Measuring Bicycle Gears

Cyclists often find it useful to have a numeric representation of the gearing provided by their bicycles. This allows them to make meaningful choices in customizing their gearing, and can be useful in comparing the performance of one bicycle with another.

There are several systems for doing this, none of them entirely satisfactory. I would like to propose a new, more accurate and more universal system.

Existing Systems

What About Crank Length?

All of these systems share a common inadequacy: none of them takes crank length into account! The fact is that a mountain bike with a 46/16 has the same gear as a road bike with a 53/19 only if they have the same length cranks. If the mountain bike has 175's and the road bike 170's, the gear on the mountain bike is really about 3% lower!

A New Standard Proposed

I would like to propose a new system, which does take crank length into account. This system is independent of units, being expressed as a pure ratio.

This ratio would be calculated as follows: divide the wheel radius by the crank length; this will yield a single radius ratio applicable to all of the gears of a given bike. The individual gear ratios are calculated as with gear inches, using this radius ratio instead of the wheel size.

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You can calculate gain ratios, gear inches or meters development with my

Online Gear Calculator or with your slide rule

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An Example:

A road bike with 170 mm cranks: (The usual generic diameter value for road wheels is 680 mm, so the radius would be 340 mm.)

340 mm / 170 mm = 2.0. (The radius ratio)

2.0 X 53 / 19 = 5.58

This number is a pure ratio, the units cancel out. I call this a "gain ratio" (with thanks to Osman Isvan for suggesting this term.) What it means is that for every inch, or kilometer, or furlong the pedal travels in its orbit around the bottom bracket, the bicycle will travel 5.58 inches, or kilometers, or furlongs.

Another example:

A mountain bike with 26 inch wheels (13 inch radius) and 6 3/4" cranks:

13" / 6 3/4" = 1.93

1.93 X 46 / 16 = 5.54

Remember, the "radius ratio" only has to be figured out once for a given bike, because it is the same in all gears. Any individual gear is calculated as:


Radius ratio X front(teeth) / rear(teeth)

Any measurement units may be used, as long as the same units are used for both the wheel diameter and crank length.

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You can calculate gain ratios, gear inches or meters development with my

Online Gear Chart or with your slide rule

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Radius Ratios for Common Crank Sizes:

Tire
Size
Tire
Radius
165 mm 170 mm 172.5 mm 175 mm 180 mm
I.S.O. 630:
27 X 1 3/8 345 2.091 2.029 2.000 1.971 1.917
27 X 1 1/4 343 2.079 2.018 1.988 1.960 1.906
27 X 1 1/8 342 2.073 2.012 1.983 1.954 1.900
27 X 1 340 2.061 2.000 1.971 1.943 1.889
I.S.O. 622:
700 X 56 370 2.242 2.176 2.145 2.114 2.056
700 X 50 365 2.212 2.147 2.116 2.086 2.023
700 X 44 354 2.145 2.082 2.052 2.023 1.967
700 X 38 347 2.103 2.041 2.012 1.983 1.927
700 X 35 345 2.091 2.029 2.00 1.971 1.917
700 X 32 342 2.073 2.012 1.983 1.954 1.900
700 X 28 336 2.036 1.976 1.948 1.920 1.867
700 X 25 335 2.030 1.971 1.942 1.914 1.861
700 X 20 332 2.012 1.953 1.925 1.897 1.844
I.S.O. 559:
26 X 2.125 330 2.000 1.941 1.913 1.886 1.833
26 X 1.9 324 1.964 1.906 1.878 1.851 1.800
26 X 1.5 312 1.891 1.835 1.809 1.783 1.733
26 X 1.25 311 1.884 1.829 1.803 1.778 1.728
26 X 1.0 (559 mm) 305 1.848 1.794 1.768 1.743 1.694
I.S.O. 571:
26 x 1 (650C) 311 1.884 1.829 1.803 1.778 1.728
Other:
Wide Tubular 338 2.048 1.988 1.959 1.931 1.878
Narrow Tubular 335 2.030 1.971 1.942 1.914 1.861
26 X 1 3/8 (590 mm) 330 2.000 1.941 1.913 1.886 1.933
24" 305 1.848 1.794 1.768 1.743 1.694
24 x 1 (520) 279 1.691 1.641 1.617 1.594 1.550
20 X 1.75 (406 mm) 254 1.539 1.494 1.472 1.451 1.411
20 X 1 1/4 (451 mm) 257 1.558 1.512 1.490 1.469 1.428
17 x 1 1/4 (369 mm) 211 1.279 1.241 1.223 1.206 1.172
16 x 1 3/8 (349 mm) 204 1.236 1.200 1.183 1.166 1.133

Thanks to Galen Evans and Osman Isvan for their assistance.

Also see my Adventure Cyclist article about gain ratios

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