Assumptions:
1.The rear tyre is loaded with the optimum Air/ Nitrogen pressure.
2.No links are removed from the chain or No modification is done on the Sprockets.
3.The RPM’s are usually considered full figures like( 666.666666=667). But in my calculation they are written as obtained like (666.6666666=666.66667)
4.The manual used is of the same motorcycle to be calculated. The versions like UG3 and UG4, V1.0 and V2.0 are not same.
5.This calculation will always be error free and accurate as the speed shown in the Tachometer. Huge difference in the RPM will be considered as the Tachometer error.
6.If the chain sprocket is not of the same vehicle, then the number of teeth in the front and rear sprocket are measured.
7.The method to calculate the RPM is same for all Motorcycles, but the value varies very much for the Royal Enfield Bullets.
8.Top gear is the highest gear in the vehicle. And the vehicle is moving with the top gear engaged.Top gear for Pulsar 220 is 5^th gear, for Duke is 6^th gear for Honda Shine is the 4^th gear.
Basic Calculations( All these data are mentioned in the Manual)
1.Final Reduction: No of teeth in rear sprocket/ No of teeth in Front sprocket. The value obtained is written upto 4 decimals if available. Varies from 2.0 to 3.5.
2.Primary Reduction: No of teeth in the Clutch/ No of teeth in the Crank gear. Varies from 3.0 to 4.0
3.Gear Ratio: They are mentioned in manual for almost all Vehicles except Bajaj. Owners having bajaj bikes please browse in the Internet. The value for the top gear ( highest gear ) is very much essential. It varies around 0.7 to 1.4.
4.The only tricky job is to find the tyre Circumference. It can be measured using a tailoring tape wound around the Rear tyre or by the method below:
a) Calculating the tyre diameter:
Basically all tires have something like this printed on it:
P315/70R17
And if we label all the number above like this:
Type Width / Ratio Radial Rim
Then the tire diameter formula is as follows:

The value obtained will be in inches and is to be converted to metre. It varies from 0.5 to 0.7.
b) Now we require to calculate the circumference. This can be done as follows. The obtained value is multiplied with π ( 22/7). Now we get the circumference in meter. Please match the value with the tape reading. It will be around 1.4 to 2.2m.
Now assume a speed of around 80KMPH. At this speed calculate the tyre RPM. This can be done as follows.

The value will be around 600 to 700 RPM.
Now the Tyre RPM for 1KMPH,

Now we can easily obtain the Engine RPM from the above data.
Calculations:

By using this method we can calculate the engine RPM at any speed. Some unknown data can also be calculated knowing the Engine RPM.
The above calculations have been tested in my Pulsar 180 and my friends Honda Unicorn. The values match with the tachometer reading in both bikes. These calculations need a small amount of technical knowledge. This might be a boring article for you. Only mechanical engineers can understand this. A simple calculation for people without technical knowledge has been given below.
1.Measure the size of the tyre with a measuring tape in meter. Mark a point on the rear tyre. Measure from that point by rotating the wheel until you get the same point again.
2.Divide 16.66667 with the obtained value. Consider it as X.
3. Now go for this calculations:

For Bikes without Tachometer,

Always Remember the value of X*R for your motorcycle. Multiplying this value with speed gives the engine RPM. This method can also be used to calibrate the tachometers for errors.
Any further queries can be mailed to me.