What the numbers mean
- Front sprocket: the small one on the gearbox output shaft (countershaft).
- Rear sprocket: the big one on the rear wheel.
- Final drive ratio: rear teeth divided by front teeth. A higher number is shorter gearing.
The formula
final drive ratio = rear teeth ÷ front teethspeed change at the same RPM = (old ratio ÷ new ratio − 1) × 100Example: going from 16/43 to 15/43. The old ratio is 43 ÷ 16 = 2.688 and the new ratio is 43 ÷ 15 = 2.867. The speed at any RPM changes by 2.688 ÷ 2.867 − 1 = −6.25%. The engine turns 6.67% faster at the same road speed. Going 16/43 to 16/45 instead gives 2.813 and −4.44%, so one tooth at the front does about as much as two or three at the rear.
Shorter or taller gearing
A smaller front sprocket or a bigger rear sprocket shortens the gearing: quicker acceleration in each gear, lower speed at a given RPM, and more RPM on the highway. A bigger front or a smaller rear does the opposite. Changing sprockets also moves your speedometer if it reads from the front sprocket or the gearbox; one that reads from the front wheel is not affected.
Speed in each gear
With the primary ratio, the gear ratios and the rear tire circumference, the speed at any RPM is:
mph = RPM ÷ (primary × gear × rear ÷ front) × circumference (in) × 60 ÷ 63,360The ratios are in your service manual. The tire size gives a nominal circumference; a real tire under load rolls a little shorter.
Chain length after a sprocket change
Each tooth added to the sprockets needs about half a link more chain. With a 520 chain and 23 inches between the axle and the countershaft, 16/43 needs 103.6 links exactly and 16/45 needs 104.7, a change of 1.08 links for 2 more teeth. Whether your current chain still fits depends on your adjuster range.
Questions
How do I calculate motorcycle gear ratio?
Divide the rear sprocket teeth by the front sprocket teeth. A 16 tooth front and a 43 tooth rear give 43 ÷ 16 = 2.69:1.
Is one tooth at the front the same as three at the rear?
Roughly, on common road bike sizes. From 16/43, dropping to 15 at the front changes speed at the same RPM by −6.25%; going to 46 at the rear changes it by −6.52%.
Does a smaller front sprocket increase top speed?
It lowers the speed the bike reaches at a given RPM by the same percentage as the ratio change. A bike that cannot reach redline in top gear may still end up about as fast, but that depends on its power and drag, not on the gearing maths.
Do I need a new chain when I change sprockets?
Adding teeth needs about half a link per tooth. Two more teeth at the rear needs about one more link, so a chain near the end of its adjusters may need two more links, since link counts go up in pairs.