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Unravelling the mysteries of ratios, gear inches, doubles, triples & compacts

I still feel that variable gears are only for people over forty-five. Isn't it better to triumph by the strength of your muscles than by the artifice of a derailleur? We are getting soft... As for me, give me a fixed gear!

—Tour de France founder Henri Desgrange

Your gears do a simple but vital job, varying the speed the rear wheel turns for a given pedalling speed. But how do you choose the right gearing for you? And how many gears do you really need?

One way or another the clever, delicate mechanism of bike gears has always been a source of controversy. Henri Desgrange, editor of Le Velo, the sports newspaper that organised the first Tour de France was not a fan, as the quote above shows. Every time component makers add another sprocket, cycling forums erupt with complaints about increasing complexity and forced obsolescence. Off-road, though, mountain bike gear systems have been driven toward simplicity, with a movement in recent years toward fewer total gears not more.

nibali riding - pic astana pro team

nibali riding - pic astana pro team

But why do we need gears anyway? What’s wrong with conquering hills “by the strength of your muscles” Desgrange-style?

The answer comes from evolutionary biology. As hunters, early humans pursued their prey till it was exhausted. We didn’t have a cheetah’s ambush ability or the sprint of a leopard, so we relied on the endurance that today lets us run marathons and ride centuries.

That means we evolved to produce a steady effort for a long time, at a fairly narrow range of power. Gears allow us to take that narrow power band and turn it into a wide range of speeds suitable for everything from grinding climbs to whooping descents.

Mechanically, the principal is simple. If one sprocket drives another via a chain, the speed of the driven sprocket comes from the ratio of the sizes. A 48-tooth large sprocket driving a 12-tooth small one gives a 4:1 gear ratio.

Foffa Urban 7 Speed Nexus - drive train

Foffa Urban 7 Speed Nexus - drive train

Working out the ratios of all your gears would tell you which were bigger and smaller, which is easier than trying to remember whether 53/16 is bigger 39/12. But you do end up with a load of very similar-looking decimal fractions.

Here’s a typical race bike gear set expressed as ratios.

  11 12 13 14 15 16 17 19 21 23 25
53 4.82 4.42 4.08 3.79 3.53 3.31 3.12 2.79 2.52 2.30 2.12
39 3.55 3.25 3.00 2.79 2.60 2.44 2.29 2.05 1.86 1.70 1.56

There are two ways of turning that ugly set of decimals into friendlier numbers. On the Continent, gears are expressed in metres of ‘development’, the distance travelled for one turn of the pedals. Here’s that gear set for a standard 700C wheel with a 25mm tyre. It yields numbers that at least have a real-world meaning, but that are still messy decimals.

Canyon Speedmax CF 9.0 SL - drive train.jpg

Canyon Speedmax CF 9.0 SL - drive train.jpg

 

  11 12 13 14 15 16 17 19 21 23 25
53 10.17 9.32 8.60 7.99 7.46 6.99 6.58 5.89 5.33 4.86 4.47
39 7.48 6.86 6.33 5.88 5.49 5.14 4.84 4.33 3.92 3.58 3.29

The alternative, still used by gear nerds in the English-speaking world, is ‘gear inches’. Here’s our race gearing chart again, in inches.

  11 12 13 14 15 16 17 19 21 23 25
53 130 119 110 102 95 89 84 75 68 62 57
39 96 88 81 75 70 66 62 55 50 46 42

Wormelow Tump (noun): Any seventeen-year-old who doesn't know about anything at all in the world other than bicycle gears.

— The Meaning of Liff by Douglas Adams and John Lloyd

You’re probably wondering where these numbers come from. The answer requires a bit of cycling history.

An Ordinary and rider (CC BY-NC 2.0 Rachel Wray:Flickr)

An Ordinary and rider (CC BY-NC 2.0 Rachel Wray:Flickr)

(CC BY-NC 2.0 Rachel Wray/Flickr)

Before bikes had equal-sized wheels and chain drives, the world of cycling was ruled by high-wheelers, the bikes often referred to as ‘penny-farthings’. Because the pedals drove the wheel directly, the gear of a high-wheeler was determined by its size.

The larger a wheel you had, the faster you could go, so riders used the largest wheel that allowed them to reach the pedals. This being Victorian England they expressed the wheel diameter in inches.

To calculate a gear in inches you multiply the raw gear ratio by the wheel diameter. That gives you the size of a high-wheeler with the same gear. Accuracy to a single inch is all that’s needed so they’re rounded.

In keeping with tradition, the nominal wheel diameter used for road bike gear inches calculations is 27in.

Gear inches give you nice, easy-to-handle numbers and I’ve a soft spot for their quaint Englishness, so that’s what we’ll use through the rest of this article.

If you want to take gear nerdiness a step further, check out this article by the late, great bicycle sage Sheldon Brown, which proposes a system for expressing gears that takes into account crank length too.

To give you some idea of what typical numbers in gear inches translate to in the real world, at a cadence of 90 rpm, the lowest gear, 42-inch, gear on our race bike will see you doing 11mph. In a 66-inch gear, you’ll be cruising along at just under 18mph, and in the top, 130-inch gear you’ll still be able to keep up with the pedals at 35mph.

Gear range & steps

The difference between the highest and lowest gears is referred to as the gear range. As you can see from our example, racing cyclists use gear set-ups with an emphasis on high gears and a relatively narrow range.

That also means the steps between gears are close. Racers like that because they can pick exactly the right gear that lets them pedal at the cadence at which they’re most comfortable and efficient, and they’re fit enough that the lack of lower gears isn’t an issue until the road gets insanely steep.

For less serious riders, gear range is probably more important. How low a gear do you need? How high?

Let’s take a look at the gear ranges you get with some typical gear set-ups.

The lower gear range you get from a compact chainset is why they have become so popular in the last decade.

  11 12 13 14 15 16 17 19 21 23 25
50 123 113 104 96 90 84 79 71 64 59 54
34 83 77 71 66 61 57 54 48 44 40 37

Throw in a slightly wider range at back at things look like this:

  11 12 13 14 15 17 19 21 23 25 28
50 123 113 104 96 90 79 71 64 59 54 48
34 83 77 71 66 61 54 48 44 40 37 33

With its WiFli transmissions, SRAM has taken this to its logical conclusion, combining a compact chainset with a very wide range cassette. 

  11 12 13 15 17 19 22 25 28 32 36
50 123 113 104 90 79 71 61 54 48 42 38
34 83 77 71 61 54 48 42 37 33 29 26

Alternatives

It’s relatively rare to find anything but a double chainset on an off-the-peg road bike, but bike makers still offer triples on touring bikes, hybrids and a few road bikes. Taking ideas from mountain bikes, some makers of cyclo-cross bikes and gravel road/adventure bikes are using single chainrings.

Shimano Tiagra triple

Shimano Tiagra triple

The advantage of a triple is that, done right, it can provide a very wide gear range with small gaps between ratios. The disadvantage is that even with the best indexed gears it can be a struggle to have the shift to the middle ring and down to the inner ring work perfectly.

Here’s a typical road bike triple set-up, as you’d get with a Tiagra triple chainset and 10-speed cassette.
 

  11 12 14 16 18 20 22 25 28 32
50 123 113 96 84 75 68 61 54 48 42
39 96 88 75 66 59 53 48 42 38 33
30 74 68 58 51 45 41 37 32 29 25

Compare that with WiFli gearing or even a standard compact and fairly wide cassette and one thing is obvious: you don’t get a much lower bottom gear for the extra complexity.

However, use the right components and you can go much lower. Here’s the gearing on a Dawes Super Galaxy tourer, which uses a Deore XT chainset intended for European 'trekking' bikes:

  11 13 15 17 19 21 23 26 30 34
46 113 96 83 73 65 59 54 48 41 37
36 88 75 65 57 51 46 42 37 32 29
26 64 54 47 41 37 33 31 27 23 21

If you’re carrying a heavy load or riding in very hilly terrain — or both — that 21-inch gear low gear will let you winch up just about anything.

It's not usual for gear freaks to custom-blend set ups that go lower still. My tandem has an 18in low gear, provided by a 20-tooth chainring and a 30-tooth sprocket.

One ring to rule them all

Single chainrings have become popular among mountain bikers for their simplicity. You can’t fluff a shift if there’s no shifting at the chainring. Racers like not having to think about front shifting, while for recreational riders who have adopted height-adjustable seatposts it declutters the handlebar.

Chainrings for double and triple cranksets are designed to make it easy for the chain to come off, so it can move to the next ring. That makes them unsuitable for use as a single rings. Chainrings with different teeth shapes, known as thick/thin rings, help solve this problem, combined with a rear derailleur that includes a clutch to stop the lower run of chain going slack.

Huge 10-42 cassette gives a massive range

Huge 10-42 cassette gives a massive range

To get a wide spread of gears, single ring systems use 10 or 11 sprockets ranging in size from tiny to huge, as you can see in the above pic. Here’s a SRAM 1X spread:

  10 12 14 16 18 21 24 28 32 36 42
44 119 99 85 74 66 57 50 42 37 33 28

The price for simplicity is that compared to other ways of getting a wide gear range there are some big gaps in there. The middle sprockets do give you a useful selection of ratios for general riding though.

If you want to play further with gear ratios and their effect on speed and cadence, there’s a great tool at gear-calculator.com

And if you've made it all the way down here, you deserve this kind of tripel:

Tripel (CC BY 2.0 Bernt Rostad:Flickr).jpg

Tripel (CC BY 2.0 Bernt Rostad/Flickr)

Tripel (CC BY 2.0 Bernt Rostad/Flickr)

Our official grumpy Northerner, John has been riding bikes for over 30 years since discovering as an uncoordinated teen that a sport could be fun if it didn't require you to catch a ball or get in the way of a hulking prop forward.

Road touring was followed by mountain biking and a career racing in the mud that was as brief as it was unsuccessful.

Somewhere along the line came the discovery that he could string a few words together, followed by the even more remarkable discovery that people were mug enough to pay for this rather than expecting him to do an honest day's work. He's pretty certain he's worked for even more bike publications than Mat Brett.

The inevitable 30-something MAMIL transition saw him shift to skinny tyres and these days he lives in Cambridge where the lack of hills is more than made up for by the headwinds.

15 comments

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VeloPeo [353 posts] 1 year ago
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Hah I was just about to comment that you should have just sent people to http://gear-calculator.com/ and it was in the last para

It really is great for comparing setups - here's a double v triple

http://gear-calculator.com/?GR=DERS&KB=34,50&RZ=12,13,14,15,16,17,19,21,...

Only non-intuitive thing for UK audiences is the "tire {sic} size" where 28" xx-622 are road tyres where the "xx" is your tyre width (so 28" 25-622 = 700x25)

 

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JorgeSilva [12 posts] 1 year ago
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Didn't understand anything  1

The "inches measurement" is what the bike moves on each pedal revolution?

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. . [175 posts] 1 year ago
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JorgeSilva wrote:

The "inches measurement" is what the bike moves on each pedal revolution?

No, it's the diameter of an equivalent penny-farthing wheel, so you need to multiply by pi to get the distance per pedal revolution.

 

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medic_ollie [43 posts] 1 year ago
1 like

You've got the cheetah and leopard mixed up in the fourth paragraph. Cheetahs run fast whereas leopards stalk.smiley

But a very useful article. Thanks

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rjfrussell [362 posts] 1 year ago
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medic_ollie wrote:

You've got the cheetah and leopard mixed up in the fourth paragraph. Cheetahs run fast whereas leopards stalk.smiley

But a very useful article. Thanks

 

gratifying to know that there is somone even more dedicated to accuracy, or pedantry, depending on one's point of view, than oneself.  I had typed a virtually identical post and then thought, "Mehhh, let it slide."  Ollie I salute your diligence!

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keirik [132 posts] 1 year ago
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I think a better article would have been, "Why do my gears always come back fromthe LBS set up worse than when they went in"

 

Seriously, I'm not sure what the point of this article is, racers will already know it, and the average cyclist won't care

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OmuGuy [23 posts] 1 year ago
2 likes

This article's supposed to enlighten beginners about gearing. 
I don't think it fulfills the brief.

The only people who understand gear inches are people who already thoroughly understand gears.
The rest of us don't give a framebuilder's curse for pennyfarthings.
And, what's so hard to understand about decimals? We all use money.

Gear inch is a jargon term, an exclusive mark of the fraternity.

Meters development and speed at NN cadence are more concrete terms that immediately mean something.
Inches mean nothing to beginners, for example, we are told "you can go much lower": 25 to 21 inches. A full four inches! We can work out a proportion but it's not a percentage or a neat fraction.

More meaningfully
34/26 = 25 inches, 2800 mm per turn of the pedal, 15.2 kph @ 90 rpm

32/30 = 21 inches, 2300 mm per turn of the pedal, 12.4 kph @ 90 rpm

A half meter difference or close to 3 kph.
For low gears, my main consideration is how slow I can go at around a cadence of 70 before I lose balance or it would be quicker to get off and push. Inches doesn't tell me that.
For high gears, looking at past data or the speeds I usually do on the flat, I can see how like likely I am to be using the highest gears for any length of time. Rather than be carrying combinations that I rarely use, to cruise comfortably, it might be better to get the ratios closer together.

Sheldon Brown's gear calculator is useful because it can be set to yield results in various ways: it yields tables after you enter the wheel/tyre, chainwheel, and cassette sizes.
These tables can be pasted into a spreadsheet. Sometimes the pasting needs a bit of finesse because the cell formatting doesn't  always stick.

Once you have tables for things like meters development and speed at 90 rpm (or whatever cadence you like), you can do comparisons that clearly mean something when you are considering changing cassettes or chainwheels, or wondering about the the abrupt jump in cadence in the middle of cruising-gear range.

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antigee [391 posts] 1 year ago
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"To calculate a gear in inches you multiply the raw gear ratio by the wheel diameter. That gives you the size of a high-wheeler with the same gear"

well I learnt something...maybe not something useful though

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crazy-legs [866 posts] 1 year ago
1 like

While I agree with some of OmuGuy's post about understanding gears I think it's a useful article for direct comparison purposes but what it needs as a follow up is something about actually using that info in practice.

So many people new to the sport use effectively two gears on their bike - as soon as the road goes even slightly uphill, they're banging it frantically down into granny gear with no real understanding that gears are there to maintain cadence.

Opposite approach on the flat or downhill when they'll be click clicking through to the 50:11 even if their cadence is down to single figures.

That makes it impossible for them to sit neatly in a chaingang or bunch, it makes them tired, they're inefficient - and they look a bit daft!

Magazines and website articles are big on power and wattage and heart rate but that comes at the cost of people looking at their powermeter and wanting to see big numbers so they bang it into the highest gear...

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Simon E [3024 posts] 1 year ago
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I'm probably a bit of a 'gear nerd' but I believe that knowledge is power (and that the accumulation of information does not equal knowledge). I'm not sure the article could be simplified without losing some of its meaning. To those who think it's superfluous: why did you read and comment negatively? (I'm presuming you did actually read it) Let's see your efforts.

I don't find numbers half as easy as a graph or chart. Here is my visual representation of triple v compact, based on Sheldon's gearing with a 700x25 wheel.

https://www.flickr.com/photos/ruralwales/23098571391/in/photostream/ligh...

OmuGuy - I type my numbers manually. Formatting the cells beforehand then Paste Special > Values in Excel should do the trick.

IME a poor chainline is not as big a deal as some would have you believe, whether you're on single or double front ring. While cross-chaining (bottom gear on the big ring or top gear on the inner) isn't recommended it's only on a triple that the angle may become an issue.

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OmuGuy [23 posts] 1 year ago
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crazy-legs wrote:

Magazines and website articles are big on power and wattage and heart rate but that comes at the cost of people looking at their powermeter and wanting to see big numbers so they bang it into the highest gear...

I hear you crazy-legs. 
If you are new to cycling, and reading Beginner's guide: understanding gears, you probably don't yet have a power meter, but you still absorb all that guff from writers. And you have fantasies about actually being able to actually use that 50/11 (or harder) on the flat... one day.
Tracking apps urge you on, too: all out, all the  time. Go for that KoM! Improve your PBs. 

Riding is biomechanical. The cheapest way to go faster (if speed is what you crave) is to reduce fat stores and improve strength (power-to-weight ratio). The next cheapest practical way is to get gears you can actually push effectively for a sustained period. It does take a while to understand with your body and mind what gears actually do.
My first real understanding of how little I actually knew came when I got a cadence meter and saw which gears I could sustain 90 rpm in and where the cadence would suddenly rise or fall by about 15. 
Perhaps my mechanical imagination is impaired, but numbers such as gear inches and ratios do not, yet, at least, mean as much to me as things like actual distance travelled or speed at constant revs.  Making a table and seeing how cassette sprockets compare on different chain wheels is really useful, especially if you have a triple up front. 

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urbane [85 posts] 1 year ago
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Power may seem fun, but too much torque on the pedals can harm your knees if they can't handle peak muscle force, as I found out the hard way, so I'm more wary about low candence now.  Viral and bacteria infections can reduce joint pressure tolerance or even cause damage via inflamation.  I tried various joint restoring supplements and am now a consumer of Bulk Powders Complete Joint Restore to ensure that my joints are protected.

I have a wide gear range triple because I need to fine tune my candence at higher speed and  climb some very steep roads and bridges.

In my opinion a fixie bicycle is retarded and masochistic nonsense, even for flatter areas because they will get stronger wind.

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Peeler [15 posts] 1 year ago
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urbane wrote:

In my opinion a fixie bicycle is retarded and masochistic nonsense, even for flatter areas because they will get stronger wind.

Unless (like a friend of mine) you don't own a car, ride 7 miles each way to work, every day, no matter the weather. Then the lack of things to go wrong is not retarded or masochistic. It's practical.
He's still a dickhead on a fixie! Ha-Ha-Ha

I could pass harsh comments about your idiocy of cycling too hard when you weren't fit enough to deal with it. But that would lead me down the same blind alley you cycled down  3

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Grizzerly [362 posts] 1 year ago
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I've been cycling for a bit over 50 years.  The impression I get from a good proportion of these comments is:

Some of you guys are missing the point,  it's supposed to be FUN!

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Peeler [15 posts] 1 year ago
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It's all voodoo and witchcraft