Sheldon Brown's
Derailer Gear/Internal-Gear Calculator
Derailer Gear/Internal-Gear Calculator
|
maintained and updated by John "Gear Head" Allen
|
|
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 under Sachs.
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.
The calculator works in any Internet broswer which supports Javascript. Turn a cell phone horizontal. The outlines of data-entry fields may be faint on a phone but they are there.
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 up to date as of August 2026 for all models which are widely known,, and some 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.
Note: results will generally be within 1% for tires with thin tread. They vary depending on air pressure and tread type. Surprisingly, tires with deep, knobby treat typically measure about 1% smaller than those with thin tread -- probably due to the relatively narrow rims commonly used with them. Fatbike tires running at very low pressure measure smaller yet, as much as 4% low compared with rollout tests. If greater accuracy matters to you, run a rollout test.
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.
Update, August 15, 2026: Tire width is now entered separately from rim diameter. This way we won't continue to get requests for tire widths we don't list!
Peter Heinle has an Excel spreadsheet online with the tooth counts of a large number of 10-through 13-speed cassettes
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 and Brompton now also has 4-sprocket version.
but other models are included in the list for the benefit of tinkerers -- see discussion.
Gain Ratios |
Gear Inches |
Meters Development |
About Percentages |
|---|
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.