Simple (?) Math for Sprocket Change - Kawasaki Versys Forum
 
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Old 04-05-2016, 01:52 PM Thread Starter
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Simple (?) Math for Sprocket Change

As a new member, my ‘search’ skills may not be as good as should be, but I couldn’t find any post on this “math” subject.

There are a few easy calculations to determine how a sprocket change will modify your performance.

As a start let’s make the following assumptions for the existing set-up on your bike:
Front (drive) Sprocket = 15 teeth existing
Rear (driven) Sprocket = 46 teeth existing
Speed @ 4000 rpm = 60 miles/hour (MPH)

Using the following formula you can calculate your RPM with a new 16 tooth front sprocket - - -
(A) RPM = 4000 rpm x 15/16 = 3750 new rpm (@60mph)
Or, with a new 14 tooth sprocket - -
(B) RPM = 4000 rpm x 15/14 = 4286 new rpm (@60mph)
Or, the ‘generic’ formula is:
New RPM = Existing rpm x existing front sprocket teeth divided by new front sprocket teeth.

Conversely, you can calculate your new speed with a new 16 tooth front sprocket - - -
(C) Speed = 60 mph x 16/15 = 64 MPH (@4000rpm)
Or, the ‘generic’ formula is:
New Speed = Existing speed x new front sprocket teeth divided by existing front sprocket teeth.

The Rear Sprocket change calculation is quite similar to the Front.
Using the following formula you can calculate your RPM with a new 44 tooth rear sprocket - - -
(D) RPM = 4000 rpm x 44/46 = 3826 new rpm (@60mph)
Or, with a new 47 tooth sprocket - -
(E) RPM = 4000 rpm x 47/46 = 4087 new rpm (@60mph)
Or, the ‘generic’ formula is:
New RPM = Existing rpm x new rear sprocket teeth divided by exiting rear sprocket teeth.

Conversely, you can calculate your speed with a new 44 tooth rear sprocket - - -
(F) Speed = 60 mph x 46/44 = 62.7 MPH (@4000rpm)
Or, the ‘generic’ formula is:
New Speed = Existing speed x existing rear sprocket teeth divided by new rear sprocket teeth.

If changing both front and rear sprockets, simply calculate, say, the front change and then the rear using the calculated new front RPM and Speed. Example, using calculations above, of changing to 16 tooth front and 44 rear sprockets.
From (A) above: RPM = 3750 (@ 60 mph)
From (C) above: Speed = 64 mph (@ 4000 rpm)
Now, factor in the rear sprocket change using the above:
Final RPM = 3750 x 44/46 = 3587 rpm (@ 60 mph)
Final Speed = 64 x 46/44 = 67 mph (@ 4000 rpm)

As long as you have any ‘baseline’ (a speed at a specific rpm) to start from, the above formulas will work for any motorcycle for which you can count the front and rear teeth.
The above formulas do not account for tach or speedo errors - - - they are just dealing with ‘indicated’ speeds and rpm’s. But, they certainly still work whether you’re dealing with ‘indicated’ or ‘actual'.
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Old 04-05-2016, 02:31 PM
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Keep in mind that the speedo is driven off the transmission output shaft, so the relationship between "indicated" speed and "indicated" RPM never changes for a specific gear regardless of sprocket choice. For instance, most of our bikes indicate about 70 mph at 5000 RPM in 6th gear. This will not change regardless of what sprockets you use.

The relationship between actual speed and actual RPM will be affected much as you've specified.
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Old 04-05-2016, 03:03 PM Thread Starter
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Excellent point!! A fact related to more 'current' motorcycles that I overlooked. My intent is to provide some tools to answer the question - - - "How much performance change will I get by changing my sprocket to X number of teeth." I used this math to determine I really wanted a 43 tooth rear sprocket on my bike. In reality, there are probably multiple calculators and charts on the Net (a good one being "gearingcommander.com") that answer that question quite nicely. Thanks for your help!!

Last edited by Curtis; 04-05-2016 at 03:18 PM. Reason: added website
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Old 04-06-2016, 12:59 PM
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I've run a 43 on the rear (with OEM stock front) for many years and have been very happy with it. Probably have done over 50k miles with this setup.

This combo makes the speedo very accurate, but the odometer under-records at about 7%.
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Old 04-08-2016, 07:07 PM
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I use my GPS speed while riding - I only look at the speedo occasionally....

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Old 04-09-2016, 12:08 AM
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if you want to play with sprockets use Gearing Commander: Motorcycle Speed, RPM, Chain & Sprockets Calculator

I went 16T up front.

It was cheaper option then 43 rear, as I got stock rear really cheap.
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