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Sheldon Brown's Internal Gear Calculator
Translation of this article: French FranceQuebec flag
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Sheldon Brown photo
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 hubs listed, and some of the cassettes, are no longer in production.
Another page omits antique and rare internal-gear hubs.

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.

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.

Want a shorter list of internal-gear hubs? Click Here!

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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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