I'm in the process of cleaning up my shop and I dug out 4 complete 8 3/4 diffs. that I have owned for 20 plus years. The tags are on 3 of the 4 diffs. so I know the gear ratios however I can't seem to pin down the ratio on the 4th unit. Can anyone provide me with a method or formula to id. the gear ratio of this mystery diff.?
Thanks in advance!!

Mark the pinion and ring gears. Rotate the pinion counting the turns so the ring gear has made 1 full revolution. The amount of turns of the pinion will be your ratio. If it turns 3 and 1/2 turns its 3.55.

It is not clear to me that you have complete third member, or button'ed up complete axles.

One caveat to what Nitrousn said is this:

What he says (for a complete axle) holds true IF you have a sure-grip or other limited slip rear. However, if the axle is NOT, you'll have to lock one axle so it won't turn, so that you can see the other move. IN THAT CASE you'll have to turn the ONE axle TWO turns to get the same result.

So----

If you have a third member, follow as Nitrousn, or else count the teeth on the pinion, the teeth on the ring, and divid ring teeth / pinion teeth.

If you have a suregrip, mark one drum and turn once

If you have an open rear, lock one axle, and turn the other side TWO turns.

Most rear ends have the ratio stamped into the outside edge of the ring gear.