Why the front sprocket is the loud one
The secondary reduction is rear teeth divided by front teeth. Nothing else. A 15 tooth countershaft sprocket with a 45 tooth rear is a 3.000 ratio, meaning the wheel turns once for every three turns of the gearbox output shaft.
Now add one tooth in each place and compare. A 16/45 is 2.813, which is 6.25 percent lower. A 15/46 is 3.067, which is 2.22 percent higher. Same single tooth, three times the effect, because a tooth is one fifteenth of the front sprocket and one forty-fifth of the rear.
The general result is that one tooth at the front is worth roughly as many rear teeth as the secondary ratio itself. On a 3.0 ratio, one front tooth moves the gearing about as much as three rear teeth. On a 4.0 ratio machine — a lot of dirt bikes and ATVs — it is closer to four.
| From 15/45 (3.000) | New ratio | Change |
|---|---|---|
| 14/45 — one off the front | 3.214 | +7.14% |
| 16/45 — one on the front | 2.813 | −6.25% |
| 15/46 — one on the rear | 3.067 | +2.22% |
| 15/48 — three on the rear | 3.200 | +6.67% |
| 15/42 — three off the rear | 2.800 | −6.67% |
That last pair is the practical point. If you want a modest change, it lives at the rear where the steps are small. If you want a large change in one move, the front does it — and then you are stuck with the size of the step, because there is no half tooth.
Which direction is which
Numerically higher secondary ratio means shorter gearing: more reduction, more torque multiplication at the wheel, more rpm for a given road speed, less speed at the rev limit. Riders say "geared down" for this and it confuses everybody, because the number went up. Fewer front teeth or more rear teeth both do it.
Numerically lower means taller gearing: fewer engine revolutions per mile, a lower cruising rpm, more theoretical top speed. The theoretical part matters. Top speed on most machines is set by the power available against aerodynamic drag, not by the rev limit in top gear. If the machine was already running out of power before it ran out of revs, taller gearing makes it slower, quieter and no faster.
The honest way to tell which case you are in is to look at what rpm the machine actually reaches in top gear on a long straight. If it hits the limiter, there is headroom for taller gearing. If it sits three quarters of the way up the range and stops climbing, drag has won and gearing will not change that.
The chain of ratios from crank to road
Between the crankshaft and the road there are three reductions in series on a chain-drive machine:
Overall ratio = primary reduction × gearbox ratio × secondary (sprocket) ratio
The primary is inside the engine, between the crank and the clutch, and it never changes. The gearbox ratio is whichever gear you are in. The secondary is the sprockets. All three multiply, so a ten percent change anywhere is a ten percent change overall.
Road speed then comes from the wheel speed and one turn of the tyre:
mph = rpm ÷ overall ratio × circumference_mm × 60 ÷ 1,609,344
With a 2.081 primary, a 0.851 top gear, a 3.000 secondary and a 1,980 mm rear tyre, 9,000 rpm gives 9,000 ÷ 5.313 = 1,694 wheel rpm, 1,694 × 1,980 = 3,354,000 mm per minute, which is 201,240,000 mm per hour, or 125.0 mph. The specification pages of the service manual are where the primary and gearbox ratios come from; nothing on this page assumes them.
What the speedometer does about it
This depends entirely on where the machine takes its speed signal, and there are two common answers. A pickup on the gearbox output shaft or on the front sprocket counts gearbox revolutions and multiplies by an assumed distance per revolution that was set with the original sprockets. Change the sprockets and that assumption is wrong by the ratio change — gear it down five percent and the speedometer reads about five percent high, and the odometer racks up miles you did not ride.
A pickup on the front wheel counts road distance directly. Sprockets are downstream of nothing it can see, so the reading does not move at all. Many machines use one and many use the other, and the only way to know is to look. This page asks rather than assuming, and if you do not know, the section is skipped rather than guessed.
Separately, a great many speedometers read optimistically from the factory. If yours already read three percent fast and you gear down five percent, the two errors add. A GPS speed on a steady road is the usual way people find out what theirs actually does.
What this calculation does not tell you
It does not know your rev limit, your power curve, your gear spacing or your chain. It reports the speed the geometry produces at the rpm you typed, which is an upper bound with no slip anywhere. Real acceleration depends on where the engine makes power relative to where the new gearing puts it, and that is a road test rather than a formula.
It also does not know whether a sprocket set fits. Rear sprockets vary in bolt pattern, offset and inner diameter; front sprockets vary in spline count and in whether a larger one clears the case and the chain guide. And the drive is a wear item that fails abruptly — a chain that leaves the sprockets at speed does damage in a fraction of a second. Chain, sprockets and adjustment are workshop matters, and the manual and a competent mechanic are the authority on all of it.
Questions people ask
Does a smaller front sprocket make a bike faster?
It makes it accelerate harder and it lowers the top speed the gearing can reach, which is not the same question. Taking one tooth off a 15 tooth countershaft sprocket raises the secondary ratio by 7.1 percent, so at any given engine speed the machine is going 7.1 percent slower and pulling 7.1 percent harder at the wheel. Whether the machine actually ends up quicker from a standstill depends on whether the shorter gearing keeps the engine nearer its strong rpm range or just adds a gearchange. Whether it loses top speed depends on whether it was reaching the rev limit in top gear beforehand. If it was already dragging out at part revs, the shorter gearing costs nothing at the top and gains everywhere else, which is why the change is so common on machines geared for a top speed nobody uses.
How many teeth on the rear equal one on the front?
Roughly the secondary ratio itself, which is a satisfying result once you see it. One front tooth changes the ratio by about one over the front tooth count; one rear tooth changes it by about one over the rear tooth count. Divide one by the other and the front count cancels into the ratio. On a 15 tooth front with a 45 tooth rear, one front tooth is worth about three rear teeth. On a 13 tooth front with a 50 tooth rear it is close to four. This is also why front sprocket changes feel like blunt instruments: there is no way to make a two percent change at the front, because the smallest step available is already six or seven percent.
Will changing sprockets throw my speedometer off?
Only if the speed signal is taken downstream of the engine and upstream of the sprockets — typically a sensor on the gearbox output shaft or reading the front sprocket. In that case the reading shifts by the same percentage as the ratio, and it shifts in the direction people find backwards: gear the machine down and the speedometer reads high, because the sensor is turning more times per mile than it was calibrated for. If the sensor is on the front wheel, sprockets make no difference to it whatsoever. The odometer moves with the speedometer, so a machine with a gearbox pickup and lower gearing accumulates miles faster than it travels them, which matters for service intervals and for anything measured in miles. A GPS speed on a level road is the cheap way to measure the real error.
Do I need a new chain when I change the rear sprocket?
Not necessarily a new one, but very likely a different length, and often a new one anyway. Adding teeth to the rear increases the chain length the geometry needs by about one pitch for every two teeth, and the axle adjusters have to make up whatever is left over. Going up several teeth can run the axle to the end of its travel with the old chain. There is also a wear argument that has nothing to do with length: a stretched chain has worn the sprockets to match its own pitch, so a new sprocket on an old chain wears quickly and an old sprocket ruins a new chain. That is why the parts are usually sold and replaced as a set. Length itself is arithmetic and is on the chain length calculator on this site.
Why did my bike get slower after gearing it taller?
Because top speed on most road machines is set by the power available against aerodynamic drag, not by the rev limit. Drag rises with the square of speed and the power to overcome it with the cube, so the last few miles per hour cost enormously. If the machine was topping out below the limiter, it had already run out of power, and taller gearing moves the engine to an even lower rpm where it makes less of it. The result is a machine that pulls to a lower speed more slowly. The test is simple: note the rpm at the machine maximum in top gear. Bouncing off the limiter means there is room for taller gearing. Stopping short of it means there is not, and the gearing is not what is limiting you.