How would you check the ratios (crown/pinion) on a rear diff?

Matter of counting the teeth?
I know you can check it if its on the car by using the dyno but what if the diff is off the car, ie confirming what you're paying is indeed what is advertised

Counting teeth on the crown and pinion is the best way

yeah, count the crown wheel teeth and pinion.

Crown wheel : Pinion

37:9 is 4.11
40:9 is 4.44
39:10 is 3.9
39:11 is 3.54

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RS Liberty - Because WRX's are only good for parts...

count the teeth thru the fill/drain plug hole(one of the 2 !)...mark one tooth with a paint pen then count away

or make a paint mark on the pinion and the CV joint and count how many turns of the pinion to one of the CV.