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  Manufacturers' literature typically gives the drive ratios of internally-geared hubs only as decimal numbers or percentages. To gain a better understanding of hubs, I examined how the internal gears produced the ratios. Gear tooth counts led to exact, fractional  ratios as given in this workbook. The results are also given as decimals. These serve to correct some minor errors in on-line and printed literature.  Ratio increments and the total range of each hub are also given as decimals, and are useful in comparing hubs. Click on the links on the title page to go to other pages in this presentation. Click on the names of hubs in the large tables or in the scrollable list at the bottom of the display to go to details for each type of hub. The workbook in its original form, including formulas used in calculation, also is available, .   
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