Modern bicycle gear systems offer up to 27 gears. However, this number is only mathematical (3 chainrings times 9 sprockets), the real gear increments are limited to around 14. Modern hub gears such as the Rohloff also manage this, Sram's i-Motion 9 and Shimano's Inter-8 are close to this.
How can I calculate the gear ratio of each gear? With derailleur gears, it's very simple: divide the teeth of the front sprocket by the teeth of the rear sprocket. Example: 36 at the front, 18 sprocket at the rear equals 2:1. This and the circumference of the wheel are used to calculate the gear ratio, i.e. the distance travelled. With a wheel circumference of two metres, one revolution of the crank therefore covers four metres.
Changing the gear ratio is limited with hub gears. This only works if you change the chainring or the sprocket on the hub gears (primary gear ratio). With derailleur gears, you can fit different sprocket sets and also change each of the front chainrings individually. However, it is important to note the gaps between the individual steps; if these are large or irregular, this is referred to as an inharmonious gear ratio. In order to be able to compare derailleur gears with hub gears, we have illustrated the gear ratios of the most common gear hubs below.
A form for derailleur gears is available at
https://www.j-berkemeier.de/Ritzelrechner.html
An Excel file for different translations for the i-Motion 9 is available as a free download.
