Speed Formulas  Gear Ratio, Tires, RPM
The parent site of this forum has a very handy speed calculator, which I've used many times. The only problem is that the calculator doesn't solve the equation for any other variable besides vehicle speed. I've rearranged the equation in four different ways so you can solve for any variable, including tire diameter, engine RPM, gear ratio, or vehicle speed. So if you know any three numbers and want to find the fourth one, use one of these equations.
In the equations, the gear ratio is stated as a single number GR, where an actual ratio is written as GR:1. Use a single number in the equation. Vehicle speed (S) is in miles per hour. Tire diameter (D) is in inches. Engine speed is RPM. 337 is a constant that needs to be there to convert between minutes and hours, and inches to miles. Just factor it in and don't worry about it.
Remember that the number to the right of the = sign is the one that you are looking for, and the ones to the left are the ones you already know, so fill them in with real numbers.
If you want to find vehicle speed:
D x RPM
________ = S
337 x GR
To find the gear ratio:
D x RPM
_________ = GR
337 x S
To find tire diameter:
337 x GR x S
__________ = D
RPM
To find engine RPM:
337 x GR x S
____________ = RPM
D
To calculate a gear ratio from a pair of sprockets, take the rear sprocket tooth count and divide by the engine sprocket tooth count. If you have a jack shaft, start with the wheel sprocket, divide by the sprocket that drives it, then multiply by the sprocket driven by the engine, and finally divide by the engine sprocket. This will give you a number which you substitute for GR in these equations.
For example, 11 teeth on the engine and 60 on the wheel will give you a ratio of 5.45 : 1, so you would use the number 5.45 to replace GR in the equations.
10 teeth on the engine, 17 on the jack shaft input sprocket, 9 for the jack shaft output, and 54 on the wheel would give you the equation GR = 54 / 9 x 17 / 10. This comes out to a 10.2 : 1 ratio, so GR = 10.2
Here's the same thing formed into a handy equation to find what sprockets to use on your jack shaft. E is the engine sprocket, W is the wheel sprocket, JI is the jack shaft input sprocket, and JO is jack shaft output.
W x JI
________ = GR
E x JO
