The one calculation behind the whole chart
Final drive ratio is the rear sprocket’s tooth count divided by the front sprocket’s tooth count. Nothing else goes into it:
final drive ratio = rear teeth ÷ front teeth
A 45-tooth rear on a 16-tooth front is 45 ÷ 16 = 2.81:1, meaning the gearbox output shaft turns 2.81 times for every turn of the rear wheel. Higher numbers are shorter gearing: more acceleration, lower top speed, more revs at any road speed. Lower numbers are taller: the reverse.
The chart below is that division worked out for every combination between a 13 and a 19-tooth front and a 38 to 54-tooth rear, which covers the great majority of what is sold as a bolt-on sprocket.
Motorcycle gear ratio chart
| Rear \ Front | 13T | 14T | 15T | 16T | 17T | 18T | 19T |
|---|---|---|---|---|---|---|---|
| 38T | 2.92 | 2.71 | 2.53 | 2.38 | 2.24 | 2.11 | 2.00 |
| 39T | 3.00 | 2.79 | 2.60 | 2.44 | 2.29 | 2.17 | 2.05 |
| 40T | 3.08 | 2.86 | 2.67 | 2.50 | 2.35 | 2.22 | 2.11 |
| 41T | 3.15 | 2.93 | 2.73 | 2.56 | 2.41 | 2.28 | 2.16 |
| 42T | 3.23 | 3.00 | 2.80 | 2.62 | 2.47 | 2.33 | 2.21 |
| 43T | 3.31 | 3.07 | 2.87 | 2.69 | 2.53 | 2.39 | 2.26 |
| 44T | 3.38 | 3.14 | 2.93 | 2.75 | 2.59 | 2.44 | 2.32 |
| 45T | 3.46 | 3.21 | 3.00 | 2.81 | 2.65 | 2.50 | 2.37 |
| 46T | 3.54 | 3.29 | 3.07 | 2.88 | 2.71 | 2.56 | 2.42 |
| 47T | 3.62 | 3.36 | 3.13 | 2.94 | 2.76 | 2.61 | 2.47 |
| 48T | 3.69 | 3.43 | 3.20 | 3.00 | 2.82 | 2.67 | 2.53 |
| 49T | 3.77 | 3.50 | 3.27 | 3.06 | 2.88 | 2.72 | 2.58 |
| 50T | 3.85 | 3.57 | 3.33 | 3.12 | 2.94 | 2.78 | 2.63 |
| 51T | 3.92 | 3.64 | 3.40 | 3.19 | 3.00 | 2.83 | 2.68 |
| 52T | 4.00 | 3.71 | 3.47 | 3.25 | 3.06 | 2.89 | 2.74 |
| 53T | 4.08 | 3.79 | 3.53 | 3.31 | 3.12 | 2.94 | 2.79 |
| 54T | 4.15 | 3.86 | 3.60 | 3.38 | 3.18 | 3.00 | 2.84 |
For a combination outside this range, or for the percentage change and the chain length that go with it, the motorcycle gearing calculator takes any tooth counts you like.
Follow the 3.00 diagonal
Look for 3.00 in the chart and you will find it six times: 13/39, 14/42, 15/45, 16/48, 17/51 and 18/54. It runs as a diagonal, and every ratio does the same thing.
That is the most useful thing in the table, because it means the same final drive ratio can be reached several ways — and those ways are not equivalent modifications. Ratio charts never say this. Three things separate cells that carry the same number:
Chain length. More teeth in total means more chain. 18/54 needs a noticeably longer chain than 13/39 at the same centre distance, and the axle sits in a different place in the adjusters. Go far enough up the diagonal and you run out of adjustment.
Wear, and this one is geometry rather than opinion. Every link has to swing through an angle as it wraps onto a sprocket, and that angle is 360 degrees divided by the tooth count:
| Front sprocket | Articulation angle per link |
|---|---|
| 13T | 27.7° |
| 14T | 25.7° |
| 15T | 24.0° |
| 16T | 22.5° |
| 17T | 21.2° |
| 18T | 20.0° |
| 19T | 18.9° |
A 13-tooth front makes every link hinge through 27.7 degrees; an 18-tooth makes it hinge through 20. The front sprocket is the small one and it turns fastest, so it is where almost all the articulation happens. Same ratio, more bending, more work into the pin and bushing surfaces. This is the reason chain manufacturers publish minimum sprocket sizes and why the bottom-left corner of the chart is hard on drivetrains.
Cost and reversibility. A front sprocket is small, cheap and takes minutes. A rear is larger, more expensive, and usually means removing the wheel. Reaching a ratio through the front is the cheap way to try it; reaching it through the rear is the way to keep the front sprocket at a size that does not chew chains.
How big a step is one tooth?
The chart shows ratios but not the size of a step, and the step is wildly uneven between the two ends. Starting from 16/45:
| Change | New combination | Ratio | Change in gearing |
|---|---|---|---|
| One tooth off the front | 15 / 45 | 3.000 | +6.7% shorter |
| One tooth on the front | 17 / 45 | 2.647 | −5.9% taller |
| One tooth on the rear | 16 / 46 | 2.875 | +2.2% shorter |
| One tooth off the rear | 16 / 44 | 2.750 | −2.2% taller |
| Three teeth on the rear | 16 / 48 | 3.000 | +6.7% shorter |
A front tooth is worth about three times a rear tooth here, which is where the workshop rule of thumb comes from. The rule is a coincidence of this particular combination, though — the exact equivalence is rear teeth ÷ (front teeth − 1), which gives 45 ÷ 15 = 3.00 for a 16/45 setup but 50 ÷ 12 = 4.17 for a 13/50 one. That derivation is set out in full on the gearing calculator page.
Note also that the front sprocket is asymmetric: taking a tooth off is a bigger change (6.7%) than adding one (5.9%), because the tooth is a larger fraction of the smaller sprocket. The rear is symmetric to a rounding error.
What the ratio does not tell you
A final drive ratio is one link in a chain of reductions, and on its own it says nothing about road speed. To get from engine revolutions to miles per hour you also need the primary reduction and the ratio of whichever gear you are in, and both of those are fixed inside the engine.
The useful consequence is the reverse of what people expect: because those internal ratios are the same before and after a sprocket change, they cancel out of any comparison. That is why you can work out exactly what a sprocket swap does to your acceleration, your revs and your speedometer without knowing a single thing about your gearbox. The chart above is enough.
Two more limits worth stating plainly:
- Ratios are not comparable between bikes. A 3.00 on one machine and a 3.00 on another are different overall gearing, because the primary and gearbox ratios differ and so do the rear wheel sizes. The chart tells you what a change does to your bike, not how your bike compares to someone else’s.
- The rear tyre is part of the gearing. A taller tyre covers more ground per revolution and acts like taller gearing. Changing tyre profile at the same time as sprockets can cancel out the change you were trying to make — motorcycle tire sizes explained covers how to read the profile off the sidewall.
Before you order
The ratio decides what happens to the bike, but three practical things decide whether the parts fit:
- Chain length has to be recalculated for the new tooth counts and rounded up to an even number of links. Both the calculation and the reason for the even number are on the gearing calculator.
- Chain pitch has to match the sprockets. Pitch is set by the chain series, and the size code tells you which — the decoding is in the motorcycle chain size chart.
- The speedometer will shift on most modern bikes, by exactly the ratio change. Whether it affects yours at all depends on where the speed sensor sits, which is covered in does changing sprockets affect your speedometer.
Sprockets and chain wear as a set and should be replaced as one, so a gearing change is usually done at chain replacement time. The wear check that tells you when that moment has arrived is in motorcycle chain adjustment, the upkeep that delays it is in how to clean and lube a motorcycle chain, and what a drivetrain service costs sits in how much a motorcycle tune-up costs.
Frequently asked questions
What is a good gear ratio for a motorcycle?
There is no single good ratio, because the number only means something relative to the bike’s internal gearing and wheel size. What matters is the direction of change: a higher number gives more acceleration and fewer miles per hour per engine revolution, a lower number gives lazier acceleration and relaxed cruising revs.
Is a higher gear ratio faster?
Faster to accelerate, not faster at the top. A higher final drive ratio multiplies torque at the rear wheel but covers less ground per engine revolution, so it shortens the gearing and lowers top speed.
Are 15/45 and 16/48 the same modification?
They give the same 3.00 final drive ratio but they are not the same change. The 16/48 needs a longer chain and moves the axle in the adjusters, while the 15-tooth front makes each chain link articulate through 24 degrees instead of 22.5, which works the chain harder.
How much difference does one tooth make?
On a 16/45 setup, one tooth off the front is a 6.7% change and one tooth on the rear is 2.2%. The front sprocket has far more effect because one tooth is a much larger fraction of a small sprocket than of a large one.
Do I need my gearbox ratios to use this chart?
No. Primary and gearbox ratios are unchanged by a sprocket swap, so they cancel out of any before-and-after comparison. They are only needed to state an absolute road speed in a specific gear at a specific engine speed.