Bike Gear Calculator

A gear ratio on its own tells you almost nothing, because the same 50/17 moves a Brompton and a road bike very different distances. The three numbers cyclists actually compare with are gear inches, metres of development and the gain ratio, and they differ in what they take into account: the first two need the wheel, and only the third knows how long your cranks are. This works out all four from the parts on your bike, along with the speed the gear gives you at whatever cadence you turn.

How it is calculated

ratio = chainring ÷ sprocket · gear inches = wheel diameter (in) × ratio · development = wheel diameter (m) × π × ratio · gain ratio = (wheel radius ÷ crank length) × ratio

Gear inches is a survival from the high-wheeler: it is the diameter the front wheel of a penny farthing would need to move you as far per pedal stroke. Development is the same idea in metres travelled per turn of the cranks. Both leave out the lever you actually push, which is why Sheldon Brown argued for the gain ratio — how far the bike moves for every unit the pedal moves in its circle — noting of the older two that "none of them takes crank length into account!". Wheel diameter here is the rim bead seat plus twice the tyre width, which is the rule his own worked examples use.

Source: Sheldon Brown, "Gain Ratios" — gear inches is "the diameter of the drive wheel, times the size of the front sprocket divided by the size of the rear sprocket"; development is "wheel diameter in meters x front sprocket x pi / rear sprocket"; the gain ratio is "Radius ratio X front(teeth) / rear(teeth)", and of the older two systems "none of them takes crank length into account!"

Questions people ask

Which of the three numbers should I use?

Gear inches if you are comparing with other riders or with published gear charts, because it is the number everybody quotes. Development if you want something physical you can picture: the metres the bike rolls for one turn of the pedals. The gain ratio if you are changing crank length, because it is the only one of the three that will notice.

How accurate is the wheel diameter?

Close, and deliberately simple. Adding twice the tyre width to the rim size assumes a tyre as tall as it is wide, which is what the worked examples in the source do. Sheldon Brown's own calculator page is more careful and says "Tire depth for a normally-inflate tire with road tread is approximately 89% of the measured tire width, but this also depends on inflation and on tread thickness and type" — which would shave roughly one percent off the development of a road wheel. You can see the size of the disagreement in his own road example: 52/13 on a 622 rim with a 33 mm tyre gives 8.646 m here and he prints 8.64, because his figure implies a wheel about half a millimetre smaller than twice the tyre width makes it. That is the whole error, in the last digit.

Does the tyre width really matter?

Less than people expect, and more than nothing. Going from a 25 mm to a 32 mm tyre on the same 622 rim takes the wheel from 672 mm to 686 mm, a little over two percent. That is worth setting correctly on a bike computer, which counts wheel revolutions, and is not worth agonising over when choosing a chainring.

Is a low gear inch number good or bad?

Neither, it is a climbing gear. The source puts the lowest gear on most mountain bikes "around 22-26 inches" and the highest gear on road racing bikes "around 108-110 inches", which is the practical span this calculator has to cover. Low numbers spin easily uphill; high numbers go fast downhill and nowhere at all up one.

Where do the rim sizes come from?

They are ISO bead seat diameters, taken from the rim size table on Sheldon Brown's gear calculator page — 622 for 700C and 29 inch, 584 for 650B, 559 for 26 inch and so on. The number is the only measurement on a tyre that means the same thing everywhere; the inch labels stamped beside it do not.

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