2012 BMW 650i 8 speed automatic Gear Ratios Calculator, MPH, Top Speed
This calculator outputs the how fast the BMW 650i can go in each gear as calculated by the gear ratios, engine redline and tire size.
The ultimate top speed may be limted by the power, drag and aerodynamics of each individual car.
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Some additional information on how these are calculated:
When D is the diameter of the tire, the car moves forward a distance πD with each revolution of the tire. If there are F revolutions per unit of time, it moves forward at a speed of πD´F per unit of time. If D is in inches and F is in revolutions per minute (rpm), the above result will be in inches per minute. There are 63,360 inches in a mile and 60 minutes in an hour, so one inch per minute equals 60/63360 miles per hour or 1/1056 mph. So we have the following formula:
V(mph) = D(in) ´ F(rpm) ´ (π/1056)
In the automotive industry, the coefficient 1056/π is usually taken to be equal to 336 (exactly it is 336.1352398...) and the formula corresponding to the above is:
(mph)(gear ratio)(336) = (tire diameter in inches)(rpm)
With the above numerical approximation, both formulas are identical if we consider that (rpm)/(gear ratio) is the rate of rotation of the tires. So the "gear ratio" as the number of rotations of the driveshaft for each turn of the tire. This ratio is normally more than 1, except in overdrive gear. So, calling R the "gear ratio", your final answer is:
V(mph) = D(in) ´ F(rpm) ´ (π/1056) / R
or, approximately: V = (D ´ F) / (336 ´ R)
where V is the velocity (in mph), D the tire diameter (in inches), F the engine rpm, and R the gear ratio.