# Multiplication of Cassette Ratios

The title can not explain it more specifically, however, recently I watched a video where I guy explains a calculation and tells the result gives how easily you climb ramps. Here is the calculation:

Rear cassette: Biggest sprocket size / smallest sprocket size Crank cassette: Biggest sprocket size / smallest sprocket size

You multiply the end results and multiply it again with 100 which gives you a percentage.

Here is an example:

Say I have a front cassette 22-32-44 and a rear cassette 11-36. The calculation is as follows:

(44/22)*(36/11)*100 = %654

So the guy says the bigger this number, the easier you climb ramps? That doesn't make ay sense to me. Does it hold any truth or does he try to mean something else?

• Your largest front sprocket tooth count divided by your smallest rear sprocket tooth count gives a number proportional to your highest gear ratio (most difficult gear). Your smallest front divided by your largest rear gives a number proportional to your lowest (easiest) gear ratio. Divide one of those ratios by the other and you get a number representing the "span" of the gears. But this third ratio, by itself, says nothing about how easy your climb is, since your "easiest" gear may be too difficult for a given hill. – Daniel R Hicks Apr 26 '17 at 1:51
• @DanielRHicks that's an answer. A low span gear might have an 11-22 cassette on the rear (also known as a corncob cassette), and a road standard chainring on the front. This would be a 100% gear range, and could be great for a flat road race. Your example is a good wide MTB range that can cope with steep grades and still have something for fast flats and descents. However your MTB answer would have tooth gaps of 2-5 teeth, whereas the flat road bike would have increments of 1 tooth between gears. (this should be a comment on Daniel's answer :) – Criggie Apr 26 '17 at 8:13

## 4 Answers

As others have already noted, the figure to which you refer pertains to the drivetrain's range, not to the lowest gear. The mechanical advantage that allows you to climb hills easily (small chainring driving your largest cassette's sprocket, say 22x36 in your example) is customarily expressed in gear-inches, a rather meaningless measure -- it indicates the equivalent diameter of a wheel that would be geared 1/1, but a standard nonetheless. 16 gear-inches would be considered small. Your example yields 15.9 gear-inches.

An excellent gear calculator can be found here. Play with it and all should become clear.

That's not calculating your lowest gear (which would determine how easily you could ride up a ramp), but the total gear range. So the difference between your fastest gear ratio and your slowest gear ratio expressed as a percent. Generally speaking a wider range means a lower lowest gear, but you could also get a higher range by making your fastest gear faster.

This page might also be useful- http://www.mbr.co.uk/news/500-gear-range-mean-drivetrain-companies-boasting-percentages-347176

The percent you get from that calculation is a way of describing the total range of a bicycle's (or other machine's) gearing, but it doesn't say anything in and of itself about exactly how low or how high the gearing is.

In other words, that 654% here is expressing that the 4:1 ratio of the 44/11 is a 654% higher gear than the 11:18. It's denoting how much variance there is in the entire system.

You don't see this way of expressing gearing used very much with derailer gears. Where it does come up is with internally geared hubs. With internal hubs you have quite a bit of freedom to use whatever cog and ring sizes you want, meaning you can "position" the range with more freedom.

That would be an indication of total gear range on the bicycle. In that example highest gear is 6.54 x lowest gear.

For climbing ability take cassette / chain ring. A 1:1 is a pretty good climber for road. For each pedal rotation one wheel rotation.

On that bike your best climb is 36 / 22 = 1.6

(44/22)*(36/11) = (36/22) / (11/44) = lowest / highest

The front is chain rings.