How to Understand Motorcycle Sprocket Math & Drive Ratios...
For most current motorcycles, the power from the engine and
transmission is delivered to the rear wheel via a drive
chain, although some models use driveshafts (many BMW's
and some Honda's come to mind), and others use belts
instead of chains (some Harleys, some Hondas, etc.).
For users of chains and sprockets, the tooth count on the front
and rear sprockets create a specific final drive ratio. This ratio
can easily be altered by changing the sprockets with replacements
that have a different tooth count. Why might you want to do this? Because
it allows you to trade some effective top-end HP for added effective low-end torque, to give
you faster acceleration (at the sacrifice of absolute top-end speed). It also permits
you to calculate a specific RPM you want the engine to be turning at your preferred
cruising speed. For example, if your motorcycle currently runs 5200 RPM at 65 mph, by
altering the tooth counts, you could push that RPM number up (to put it further into the
powerband for better roll-on performance) or down (to reduce vibration and improve fuel
mileage/tank range if you do lots of highway driving).
TYPES OF MODERN SPROCKETS:
Just as modern chains come in a variety of widths, sprockets come in matched widths
for use with specific chains. If you use a #530 chain, use sprockets designed to work
with a #530 chain. For more information on chains, see
How to understand Motorcycle Chains, Wear and Maintenance.
The primary differences between sprockets are the width (mentioned above -- match to your chain), the tooth count, and
the material that the sprocket itself is made of. Almost all motorcycle manufacturers ship their bikes with steel sprockets
as standard OEM sprockets, because steel is both cost-effective (cheap to buy) and long-lasting (less prone to wear than
other standard sprocket metals). Many aftermarket sprocket manufacturers offer replacement sprockets made of high-grade aluminums,
sometimes with an additional hardening coating on the exterior. The sole advantage of aluminum (as far as I have been able to
determine) is the weight, since it usually both costs more and wears out much faster. Even if the surface of the aluminum is
hardened (anodized), the subsurface aluminum still has to carry a load and does deform faster than steel. Some aftermarket
manufacturers are getting around this by marrying steel sprocket rings to aluminum carrier hubs, for the best of both worlds.
There are only two basic equations for sprocket math: calculating the sprocket drive ratio and calculating the percentage change in sprocket
Calculating the sprocket drive ratio:
(Rear tooth count) / (front tooth count) = drive ratio
Bike ships stock with 47 tooth rear sprocket, 15 tooth front sprocket.
47 / 15 = 3.13333
So 3.13333 is the stock sprocket ratio.
You buy a 50 tooth rear sprocket and a 15 tooth front sprocket for the above bike.
50 / 15 = 3.33333
So 3.33333 is the new sprocket ratio.
Calculating the percentage change in sprocket ratios:
((new ratio / old Ratio) - 1) * 100 = change as a percentage.
NOTE: Positive percentages indicate higher gearing ratios, negative numbers mean lower gearing ratios
Example (using the numbers from the first set of equations):
Motorcycle had a 3.1333 sprocket ratio,
cycle will now have a 3.3333 sprocket ratio
((3.3333 / 3.1333) - 1) * 100) =
((1.0638) - 1) * 100) =
(.0638) * 100) = 6.38% change
Combining the equations (if you'd want to for some reason):
(( (NewRear/NewFront) / (OldRear/OldFront) ) - 1) * 100 = % change.
Example (using the same numbers as from the sprocket drive ratio examples):
(( (50 / 15) / (47 / 15) ) - 1) * 100 =
(( 3.3333 / 3.1333 ) - 1 ) * 100 =
(1.0638 - 1) * 100 =
(0.0638) * 100 = 6.38
Thus, changing from 47 to 50 tooth rear with a 15 tooth front is a 6.38% change.
IMPORTANT SPECIAL NOTES:
- The Percentage change is the increase or decrease in available torque
compared to stock. It is also the percentage that your RPM's will
increase/decrease for any given steady speed (i.e. - if stock is 5000 RPM at 67
MPH, a 10% change will make the RPMs 5500 at 67 MPH. Additionally, if your bike
reads the speed off the front sprocket, your speedo will be
off by this amount as well. There are two products on the market to that I know of correct for
this inaccuracy: the SpeedoHealer
and the YellowBox.
- By altering the sprocket ratios to a positive percentage change, you are
trading some effective top-end HP for effective low-end torque. Torque
primarily affects acceleration between 0 and about 65 mph, while effective HP
affects primarily speeds above 65 (especially top speed), and the ability to
counteract wind resistance. If your bike can reach speeds above 100 MPH, expect
a 12% - 15% change to cut around 15 - 20 MPH off your top speed, because that
HP you've traded is critical to overcoming the wind resistance at high speeds.
Also expect seriously degraded fuel-mileage as a result of the
- By altering the sprocket ratios to a negative percentage change, you are
trading some effective torque for increased effective HP, but this is likely to
only alter your gas mileage at steady cruising speeds, not increase your top
speed, as the actual total HP for the bike has not increased. The primary
reason for going with a negative percentage change is to reduce the RPM's
required to cruise at whatever standard cruising speed you ride at if you do a
lot of long-haul touring or commuting (e.g. - getting you out of a zone of vibration
if you happen to normally cruise right at the same RPM that the bike vibrates the most).
- Large percentage (more than 8% or so) changes in either direction (from stock) can produce undesirable results.
Large positive percentage changes
can cut your top speed significantly, reduce your effective traction under high throttle applications, and may cause the front
end to become light or wheelie in response to the increase in torque.
Large negative percentage changes can actually increase your
gas mileage if you are not cruising steady (as you try to compensate for sluggish performance by giving it
more gas during acceleration), and will reduce your rate of acceleration
(including out of a dangerous situations).
- Changes under 3% from the current ratio are not likely to be noticed by
- Whenever feasible to obtain a specific ratio, avoid using a smaller than
stock front sprocket. The smaller sprocket requires the links of the chain to
turn a tighter radius, which increases friction and decreases the life
expectancy of the chain (by decreasing the life-expectancy of the o-ring seals
of the chain).
- Adding sprockets with additional teeth will require a chain with a higher link count to compensate
for the longer path the chain now needs to take. Using sprockets with fewer teeth will require a chain with
less links to cover the same adjustment range.
- Unless you very recently replaced your chain, always replace chains when replacing sprockets (and visa-versa). The two
surfaces are designed to mate and wear together (the sprocket-tooth/chain-roller interface) and use of a new sprocket with
a worn chain can quickly ruin the sprocket... similarly, use of a worn sprocket with a new chain will quickly ruin the chain.
- Katana/Bandit owners can see this premade chart of sprocket ratios for quick