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There are several ways:
o Decode the code on your vehicle ID plate (post the info & you will be helped)
o Read the tag on the axle housing (it will probably be covered with grease)
o Jack up one wheel & put the axle on a SAFE stand; mark the driveshaft and the free wheel with a piece of chalk; have an aid rotate the wheel TWENTY turns; divide the number of turns the drive shaft turns by TEN and you will have the ratio (accurately).
Not sure I understand your math. Using a 4-to-1 ratio for simplicity, the driveshaft would have turned 80 times after turning the wheel 20 times; dividing 80 by 10 gives you double the actual ratio, or 8 instead of 4.
Unless I am wrong (it could happen) the apparent error comes from the differential action. This is where the 2:1 difference is coming from in your example. If one wheel is on the ground (not turning), the other turns twice as many turns in order to drive the ring gear the the same amount as if both wheels were turning. (Remember, the axles are driving the side gears, not the differential carrier/ring gear.)
Now you've got me thinkin'; I'll definitely have to check this out the next time I rotate tires! I wonder if the same applies to LS rear ends with 1 tire on the ground?
With a limited slip, you will have to overcome clutch friction to do the 20-turn method, which will be a lot in a fresh system. In this case, I recommend you put both ends of the axle on stands and do only ten turns. (This is what you wanted to hear anyway!)
I only do the 20 turns because I am to lazy to jack up both sides.
I like to get the truck on very level ground or garage floor, and roll it one tire revolution, while counting the driveshaft revolutions. That way you don't have to be concerned with jacking the truck up or counting one wheel or two wheels. JMO
I like to do the twenty turns to be sure to separate ratios that are close together, such as 3.70 and 3.89. (I have never been able to do this by myself - keeping track of the wheel AND the shaft always results in confusion. My wife still thinks this is some strange ritual that men perform.)
Reading the tag is easiest IF it is the correct one, and you can't beat actually counting the R&P teeth for ultimate in accuracy.
What truck do you have?, A lot of the tech threads have a thread that will decode the door sticker & give you that information. In the superduty thread it is the first post