How to Understand Motorcycle Sprocket Math & Drive Ratios...

PURPOSE:
 
   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.

SPROCKET MATH

  There are only two basic equations for sprocket math: calculating the sprocket drive ratio and calculating the percentage change in sprocket ratios.

Calculating the sprocket drive ratio:
 
(Rear tooth count) / (front tooth count) = drive ratio
 
Example 1:
Bike ships stock with 47 tooth rear sprocket, 15 tooth front sprocket.
47 / 15 = 3.13333
So 3.13333 is the stock sprocket ratio.
 
Example 2:
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 trade-off.
   
• 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 the rider.
   
• 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 reference.