# Why are bicycle gear ratios computed as front/rear and not the opposite?

I recently realized that when people talk about bicycle gear ratios, it's calculated as number of teeth on the (front) chainring divided by the number of teeth on the (rear) sprocket/cog.

This made me a bit confused, because I was thinking that gear ratios are usually the opposite - driven gear/sprocket/pulley divided by the driver (e.g. motor). When talking about motorcycle final drive, the formula is rear/front sprocket teeth. When reading motorcycle/car specs, the lowest gears - 1st gear and reverse - have the highest numbers.

I tried to find why it's the opposite with bicycles, but so far couldn't...

Can someone shed some light on this topic? How this came to be historically?

• Gear ratio is largely irrelevant. The important number is gear inches. – Daniel R Hicks Feb 9 at 23:43
• Gene also consider that bicycles came first, so really motor cycles flipped the convention, for some reason, after the fact. – Criggie Feb 10 at 0:20
• @Criggie I'm not sure what VAM has to do with Gene's question but I'm really here to say that's not French, it's Italian. – R. Chung Feb 10 at 4:27
• @Davor - Wheels aren't all one size. – Daniel R Hicks Feb 12 at 19:35
• Guys let's keep it respectful. Generally speaking, there are indeed a variety of wheel sizes even within one discipline (e.g. 29", 27.5" and 26" mountain bike wheel standards). So if someone wants to compare the overall gearing of two different bikes (e.g. switching from an out-of-fashion 26" mtb to a bigger size one), the wheel size must be taken into account. In the same way when putting larger wheels on an offroad car, the max torque at the wheels is reduced, so a lower final drive gearing might need to be considered if the wheels are significantly larger. – Gene Pavlovsky Feb 17 at 14:47

I think it's simpler than what many think.

Car and motorcycle drivetrain is a reductor: their ratio (driver to wheel) < 1 in most cases. Bicycles are the opposite: the wheel normally turns faster than the cranks, and the drivetrain is a multiplier.

It is somehow easier to remember and 'feel' ratios that are greater than 1: compare `4.3, 3.7, 2.9` with `0.23, 0.27, 0.34`. So that's how it's done.

In the end, this is the same argument: tradition. But at least this is an attempt to explain how such tradition came about.

Besides, cyclists rarely operate ratios per se. We may fancy with 'proper' units like gain ratios etc. mentioned in other answers, when selecting a new cassette, but in practice we just know it by the teeth :) Tell me any standard ratio expressed in teeth (say, 39/17), and I'll immediately say at which speed I will use it and how 'hard' it is. Yet I don't even know what ratio it is without a calculator.

• Thanks, nice answer. Unlike you, I wouldn't be to tell how 39/17 (or the equivalent ratio) feels. I just know how the gears currently on my bike feel, and which I would ride on which terrain. I'm converting from 3x9 (44-32-22 chainrings, 11-28 cassette) to 1x11 drivetrain. Choosing a cassette was pretty easy (10-42T), so I just had to choose the chainring. I wanted my lowest gear to be as low or lower than now. Calculating gear ratios was a good way to figure this out, and also to see how much I will sacrifice in high gear. – Gene Pavlovsky Feb 10 at 12:43
• I ended up with a 32T chainring, giving a 3% lower lowest gear, and sacrificing 20% on the highest gear. I didn't install the parts yet, it remains to be seen if I will be happy with this setup. – Gene Pavlovsky Feb 10 at 12:46
• I think your answer is likely right. Searching for exact definitions of the term "gear ratio" turns up mostly similar results, e.g. "the ratio of the turning speed of the powered gear to that of the final gear" (opposite of bicycle convention). I've also found this conflicting definition "The gear ratio is the ratio of the number of teeth in the gear to the number of teeth in the pinion, the pinion being the smaller of the two gears in mesh" - which makes sense for both bicycle and mechanical conventions, but doesn't tell us is the gearing system is reducing or multiplying. – Gene Pavlovsky Feb 10 at 12:53
• Re "It is somehow easier to remember and 'feel' ratios that are greater than 1", Maybe when expressed as a decimal, but not when expressed as a ratio – ikegami Feb 11 at 18:33
• @ikegami I think it's pretty difficult to compare gear ratios expressed as ratios, e.g. 32/13 vs 44/18 - which one is larger, and by how many %? (Two real actual gears on my bike). When expressed as decimals, easy to compare. – Gene Pavlovsky Feb 12 at 16:16

When talking about bicycle gearing, the overall theme (in my mind) is translating rotations of the crank to distance traveled. Historically, I believe this was used to translate the gearing of "safety" bicycles (what we now ride) to the size of the larger wheels on the old penny-farthing highwheelers. In that case, you multiply the gear ratio by the wheel diameter to estimate the equivalent penny-farthing wheel size.

Nowadays, using the chainring as the numerator lets you multiply the gear ratio by your cadence (rate at which you're turning the cranks) and your outer tire circumference to compute your speed.

You could easily flip the ratio if you wanted. But now to compute the speed you'd multiply your cadence by the tire circumference and the divide by your inverted gear ratio.

• A reference to gear inches as a measurement for comparison of bicycles seems relevant, especially since it ties back to penny-farthings. Ultimately, gear ratio (as computed for bikes) is based on that calculation without the wheel size factor, since that can vary even on the same bike based on the particular tires mounted. – DavidW Feb 9 at 23:09
• I like that this answer focuses on the "why is it front over rear, not rear over front" question without getting distracted by the side issue of "counting teeth or counting number of rotations", which cancels out in the ratio. – RLH Feb 10 at 1:45

The front-over-rear ratio for the drive train on a bicycle describes how much faster the rear wheel turns than the rider's cadence.

The rear-over-front ratio for the drive train on a motorcycle describes how much more torque the drive train can produce at the rear wheel than at the motor.

It is of course matter of convention which is used, but I would posit that because

1. To the rider, the bicycle is a mechanical augmentation of the human body and
2. In locomotion, the human body is speed-constrained rather than force-constrained,

the ratio that describes how much more speed the bicycle allows is the natural measure of its drive train.

Conversely, I would posit that

1. To the rider, a motorcycle is a means of turning fuel into motion, and
2. Internal combustion engines are better at producing speed than they are at producing torque,

so that the ratio that describes how much more torque the drive train produces than the raw engine becomes a more natural measure of the drivetrain.

• I think your answer makes good sense. The torque multiplication sense is used mostly everywhere in engineering and mechanics, not just motorbikes. But I guess the reasoning is the same. Most of the time it's some kind of motor turning an output shaft that should rotate more slowly. Most gearboxes are reduction gearboxes. There are much fewer cases of speed multiplication gearboxes, bicycles apparently being one of them. I just didn't think of that point :) – Gene Pavlovsky Feb 10 at 12:58
• This. On a bicycle, you keep the cadence constant(ish), using different gears to select the highest speed for the power you're willing to invest; on a motorbike, you rather keep the speed constant, using different gears to select the lowest RPM which can provide enough power to accomplish that. – leftaroundabout Feb 11 at 13:13

Right now we have a single standard of `frontteeth:rearteeth` like 53:11 and 30:34, which has been around for many decades. But does not account for wheel diameter or crank length.

So we get another standard which is Gain Ratio

And we still have an old-school notation of Gear Inches from the high-roller bikes so there's some consistency over time.

Additionally `metres/yards/feet developed (per crank rotation)` is known as Development or Rolllout are a more recent way of showing the same info, along with `RPM at speed X` and `speed at RPM Y`

Ultimately it comes down to tradition - early bicycles had a fixed chainring size and perhaps two cogs on a rear hub that could be flipped. So your gear ratio was stated with the fixed unchangeable part first (ie you wouldn't swap chainring on a ride, whereas you might flip the rear wheel for the other gearing.)

Some people use Percentages but that is specific to a cassette and has no bearing on the chainring side of things.

And also because https://xkcd.com/927/ If you choose to flip an existing standard around, absolutely utterly make it unique in notation to avoid confusion. A hypothetical "11:53" is not the same as 53:11 and imparts exactly no more useful information. Do read and understand https://xkcd.com/1179/ and comprehend just how much enmity people who use YYYY-DD-MM earn themselves.

• My personal bête noire is MM-DD-YYYY which is far too common among people in the US. :-P To the point that some bright light at our customer changed the database's default standard date representation to that garbage! Argh! – DavidW Feb 10 at 0:55
• @DavidW I wouldn't personally admit to intentionally misreading dates like that at work, while demonstrating the use of clear formats like 2021-02-03 or Feb 3, 2021... some of my coworkers read this :) – Criggie Feb 10 at 4:23
• Anyone managing to make a relevant link to XKCD deserves a +1. – Jyrki Lahtonen Feb 10 at 11:22
• Is YYYY-DD-MM even legal? I think if it starts with the 4-digit year, it must be YYYY-MM-DD. Which makes total sense unlike the other options :) – Gene Pavlovsky Feb 10 at 13:02
• What can you expect from a world where people talk about the sun setting when actually it is the horizon rising? – user3067860 Feb 10 at 20:25

On a car, first gear might be 5:1. Five (input) rotations of the crankshaft for one (output) rotation of the propshaft. This tells you nothing of the number of teeth that are actually used on the gears. One a bike, we express the gearing in terms of teeth front and rear, eg 39/13. Not the number of rotations. This is more useful for calculating gear-inches or development, which is how we normally express ratios--if we expressed the gear as 13/39, we'd then need to take the inverse of that before calculating gear-inches anyhow: 1/(13/39).

In brief, `rotations:tooth counts::apples:oranges`

• It makes sense. But I needed to use decimal gear ratios to figure out which chainring to get for a 3x9 to 1x11 conversion. I wanted not to lose any low-gear torque, and I also wanted to know how much high-gear speed I would sacrifice. – Gene Pavlovsky Feb 10 at 13:04