Editors Note: 'Science Behind the Magic' delves into the inner workings of your two-wheeled steed. Art's Cyclery web content editor Brett Murphy uses his mechanical engineering background to explain the latest industry advances and breakdown the inner workings of common components. The original article can be found here.

I recently wrote reviews of the e*thirteen Extended Cog and GuideRing M after converting my own bike to a 1×10. I had great things to say, and have received some requests to further discuss 1×10 gear ratios, including extended cog range setups. I thought it would be useful to compare some stock setups with the 1×10 extended range possibilities. Comparing the gear ratios and the cost differences should help you make an informed decision about where to spend your money.

This recent survey on Mtbr shows the popularity of 1x10 Narrow/Wide conversion drivetrains.

This recent survey on Mtbr shows the popularity of 1x10 narrow/wide conversion drivetrains (click to enlarge).​

The growing popularity of extended cogs is a result of 11-speed 1x drivetrains by SRAM and Shimano. There are mechanical and weight advantages to ditching the front derailleur in favor of a wider range cassette that can do the job of a double or triple chainring system. The manufacturers have decided however that these wide range cassettes should come with a hefty price tag and the requirement for a new shifter, derailleur, and potentially a new freehub body or hub. E*thirteen, Hope, and others all have extended cogs that increase the range of your current 10-speed system by adding a 40 or 42-tooth cog to the freehub body; making room by removing the 15T or 17T cog on the existing cassette.


The following graphical representation shows a comparison of gearing between four setups. The X-Axis is arbitrary and represents the number of gears available. A 3x system has 30 gears to choose from, however most of them overlap and are redundant. The Y-Axis shows the number of centimeters of forward movement per crank revolution. Rolling centimeters are calculated by multiplying the circumference of a 29-inch tire by the gain ratios of the gearing.

Gearing Chart

The jumps in rolling distance observed in the 3x (blue plot) and 2x (red plot) show the change from one chainring to the next. While 3x does offer a slightly better range of gearing, the amount of redundancy in gear ratios is extreme. Comparing the 24T ring of the triple to the 32T ring, you can see that the first 8 high gears overlap in rolling distance to gearing in the 24T ring. Only the last two shifts offer a new ratio. The same is true of the 42T ring. Of the 30 gearing choices on a triple 10-speed setup, only 14 combinations offer unique gearing, the rest are redundant. The same is true of a double but to a lesser degree. Of the 20 gearing combinations on a double, 14 are unique ratios. Doubles offer an almost identical range of a triple with one less ring.

The typical 1×10 conversion drivetrain involves removing the 15 or 17 tooth cog and adding in the 42 tooth after the 36. The front chainrings and derailleur are removed in favor a 32 tooth Narrow/Wide front chainring.

The typical 1×10 conversion drivetrain involves removing the 15 or 17 tooth cog and adding in the 42 tooth after the 36. The front chainrings and derailleur are removed in favor a 32t narrow/wide front chainring.​

The major concern for most people when moving to a 1x system is that they will be losing gears, making it harder to climb. I set up the gearing in the chart so that all combinations would have approximately the same gearing for climbing. All setups have roughly 150 centimeters of forward movement per pedal stroke in the lowest gear. So let's set that concern aside, it will be just as easy to climb with your new extended range (42t) 1×10 as any other factory setup. Now on the high end of the gear range there is a bit of a different story to be told. The 3×10 setup wins the highest gear award with the ability to move 878cm per pedal stroke and the 1×10 comes in last at 627cm. This explains some of the reasoning behind SRAM's XD freehub body that allows for a 10-tooth cog, which increases high-end ratios.

Now before dismissing the 1x setup on account of a lack of high gearing, ask yourself if you really think you've ever used this range before. Looking again at the chart, we can see that the same ratio of a 1×10 extended setup (30T ring in the 11T cog) is available with a 3×10 setup using the 42T ring with the 15T cog. So take your current 3×10 bike out for a ride, and when you are descending the trails or riding back to the car on the flats, see if those last two gears (the 13 and 11-tooth cogs) make a difference to you. From personal experience, I find I don't have an issue spinning out on my bicycle. At 90RPM this last gear would have you traveling at 30mph. While I do have loads of fun ripping trails at 30mph, I don't find myself pedaling in these situations and also don't spend time on the road spinning at this speed.

Depending on your bicycle and riding style, perhaps higher RPMs and speeds are more important to you. Check out some of the pro XC setups around today. For the most part they are running an XX1 10-42 cassette with either a 36T or even a 38T chainring. So perhaps if you are building a XC rig, you look at a bigger front ring paired with that 10-speed extended cassette. Below we can see the results of the new 1×10 11-42T cassette with a 36T chainring stacked against the original triple and 30T 1×10 setups. Shifting the line upwards in favor of higher speeds and less climbing.

1x10 36T


Continue to page 2 for calculations and the bottom line »


Looking at some of the bicycles currently in the Art's inventory, I've found some general gearing trends for today's mountain rides: 3×10 setups are on the budget conscious bikes, 2×10 on mid-range bicycles, and 1×11 on the top-end models. The 3x bikes usually have a 24/32/42 chainring setup, while 2×10's sport a 24/38-tooth setup. Regardless of the number of front chainrings, an 11-36T 10-speed cassette seems to be the norm in the rear. The 11-speed setups tend to include either a 30 or 32T front cog with a 10-42T in the back. These are not hard-and-fast rules, just some general trends used to evaluate drivetrains for the purposes of this article.

When comparing, the first thing to do is divide the number of teeth up front by the number in the rear of the currently selected cog. This gives you the gain ratio of the system and tells how many times the wheel will rotate per revolution of the crank. The data below shows the gain ratios of 3×10, 2×10, 1×10, and 1×11 systems.

Gain Ratios

One thing this data doesn't take into account is the size of the wheel. I'm sure there are plenty of you out there that are still rocking 26-inch wheels, while your friends run 27.5 wheels or 29ers. By multiplying the gain ratio by the circumference of the tire, we can calculate the distance the bicycle will travel for every pedal stroke. Because 26-inch wheels have a smaller circumference, we can step up the gearing so that it will roll the same distance in all gears. The math is there for you to double check, but a general rule of thumb is to step down 2 teeth in a chainring for every wheel size. So while I'm happy with the 34-tooth ring on my 26in bike, I would probably switch to a 32-tooth on a 27.5 bike with the same cassette, or a 30-tooth on a 29er. The below tables show the centimeters of forward movement for every pedal stroke on a 29er tire with a 30T ring compared to a 27.5 tire and 32-tooth ring.

1x10 Distance Traveled per Pedal Stroke

Bottom Line

Now that we've done a bit of analysis on gear ratios, you might be almost convinced to make the switch, but lets look at things from a monetary angle. The costs involved in a new extended range 1×10 drivetrain really depend on your current equipment. A rear derailleur with a clutch is a requirement, along with either a narrow wide chainring or a chain guide. Without a front derailleur, the clutch derailleur and tall chainring tooth profile are necessary to keep the chain in place. If you already have these items, you might get away with just buying the extended cog. Because everyone's situation will be different, the table below list prices and weights on every component (you might not need every component) and then compares to an entry level X1 11-speed system.

Price and Weight Breakdown for 10 and 11-speed

10-Speed Price10-Speed Weight11-Speed Price11-Speed Weight
DerailleurShimano XT M781 $69.99237 gramsSRAM X-1 Type 2.1 $230.99257 grams
Cassettee*thirteen Extended Cog $65.99367 grams (w/ XT Cassette)SRAM X1 XG-1180 $245.00312 grams
ShifterShimano Zee M640 $34.99142 gramsSRAM X1 Trigger Shifter $69.99123 grams
Chainringe*thirteen GuideRing M $43.9943 gramse*thirteen GuideRing M $43.9943 grams
Totals$214.96789 grams$589.97735 grams

The end result is an additional $375 for an X1 drivetrain over a custom 1×10 setup, saving a total of 54 grams. I leave the decision to you my friend, but I will personally be waiting for 11-speed drivetrains to trickle their way down into less expensive component groups. [Editor's Note: SRAM may well have answered this call with its new, more affordable GX drivetrain, which debuted after this article was written.]