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Sheldon Brown's
Derailer and Internal-Gear Calculator
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by Sheldon "Gain Ratio" Brown
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You need to enter data for at least one chainring, and at least
one sprocket unless you choose a stock cassette.
Listing of internal hubs is A>Z by manufacturer, then by number of speeds, type and age.
Fichtel & Sachs, Sachs and SRAM are the same series of hubs, shown together.
This page covers most internal hubs back to the original 1902 Sturmey-Archer
Many of the internal-gear hubs listed, and some of the cassettes, are no longer in production.

Clicking on "calculate" generates two new output pages: a full-size one, and a small one which you might print out and tape to your bicycle's handlebar stem for reference. The small one will overlay the large one in a browser which supports tabs.

If you do a calculation, then bring those to the front, subsequent "results" windows from subsequent calculations may be hidden behind them.

For multiple calculations, you should close each set of results in turn, not hide them.

Cassettes listed are Shimano unless otherwise indicated.

The selection of internal-gear hubs in the Calculator is complete except for one or two new models whose gear ratios have not been made public, and some very rare antiques. The selection of cassettes is fairly complete for Shimano, SRAM and SunRace. For brands and models not covered, or if building up a custom cassette, you will need to count sprocket teeth and enter the tooth counts under "custom sprockets." Our cassette page links to additional information on cassette tooth counts.

If you're using a Schlumpf Drive plus a geared rear (internal or not) hub you should enter the actual number of teeth of the front chainring for the first chainring, and this number of teeth times the Schlumpf ratio for the second chainring. The ratios are 0.40 for the Mountain drive, 1.65 for the Speed Drive, and 2.50 for the High Speed Drive.

Wheel Size
Crank Length
Gear units
or Cassette
Custom Sprocket(s)
(1 or more)
Internal Hub

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The SRAM/Sachs 3 x 7, 3 x 8 and 3 x 9 and the Sturmey-Archer CS-RF3 and CS-RK3
are the only production internal-gear hubs designed to use rear sprocket clusters;
The Sturmey-Archer-Brompton BWR takes two sprockets,
but other models are included in the list for the benefit of tinkerers -- see discussion.

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Too High-tech for you? You can use your slide rule instead!

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Gain Ratios

Gear Inches

Meters Development

About Percentages

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Thanks to Stephen D. Cohen and Timothy Lipetz for programming help.

Problems with this program? You need a browser with JavaScript. This program generates a new window with the results of each calculation. If your browser has a "pop-up blocker" activated, it may prevent the results window from opening.

If you do a calculation, get a result, then bring this window to the front, subsequent "results" windows from subsequent calculations may be hidden behind this window.

For multiple calculations, you should close each "results" window in turn, not hide them.

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Further information:

If you want more numbers, including speed and cadence data,
Jake Odell has a more elaborate gear calculator:

HPV Drivetrain Analyzer

Tom Kunicki has a calculator with specific features useful for fixed-gear and singlespeed riders:

"Rabbit, A Singlespeed and Fixed-gear Calculator"

John Allen has pages giving exact, fractional ratios calculated from gear tooth counts:

"Drive ratios of bicycle hub gears"

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