Suppose your motor vehicles speedometer not working and you need to know your vehicle speed for the given engine speed for a certain gear ratio. How you can do that , let’s see..
Say, Engine rpm= 3000
Axle ratio = 4
Tyre size = 12 inch radius
The formula for calculating vehicle speed is:
Car or automobile speed in consistent unit,
V = (engine rpm * wheel tyre perimeter)/(gear ratio * axle ratio)
Or, V = (engine rpm * 3.14 * tyre diameter ) / ( gear ratio * wheel axle ratio)
For the given values,
V = (3000 rpm* 3.14 * 2 * 12 inch) / ( 1.5 * 4)
Or, V (kmph)= (3000 * 60 rph * 3.14 * 2 * 12 * 25.4 * 0.000001 km)/(1.5 * 4)
Or, V = 57.42 kmph
Now as you know the equation for calculating vehicle speed given the engine rotation speed, you can easily find out the engine rpm of your car if you the vehicle speed from your speedo.