Accessories Bicycles Parts Specials Tools

Sheldon Brown's
Derailer Gear/Internal-Gear Calculator
Translation of this article:
French FranceQuebec flag
German German flag
find us on FB

Sheldon Brown photo
by Sheldon "Gain Ratio" Brown
Spoke Divider

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 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.

The selection of internal-gear hubs in the Calculator is complete except for one a few new models whose gear ratios have not been made public, and some very rare antiques. The selection of cassettes is up to date as of February 2018 for Shimano, SRAM, SunRace and recent Campagnolo models. 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 an internal-gear rear 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.

Peter Heinle has an Excel spreadsheet online with the tooth counts of a large number of 10-through 13-speed cassettes

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

Spoke Divider

The SRAM/Sachs 3 x 7, 3 x 8, 3 x 9, 3 x 10 and the Sturmey-Archer CS- RF3 and CS-RK3
are the only recent/current 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.

Spoke Divider

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

Spoke Divider

Gain Ratios

Gear Inches

Meters Development

About Percentages

Spoke Divider

Spoke Divider

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.

Spoke Divider

Further information:

RPM range vs. speed is given in

Mike Sherman's gear calculator.

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

HPV Drivetrain Analyzer (note -- the page is available in the Internat archive but the calculator doesn't work).

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"

Spoke Divider

Spoke Divider

Articles by Sheldon Brown and Others

Accessories Bicycles Parts Specials Tools

Copyright © 1998, 2008 Sheldon Brown

Harris Cyclery Home Page

If you would like to make a link or bookmark to this page, the URL is:
Last Updated: by John Allen