Of course, you don't have to count the teeth, because the numbers are stamped on the side of the ring gear. But if you've already popped the cover, why not count? You probably need to change the gear oil anyway, but if you don't want to drain, clean, form a new gasket, refill, etc. just to check the gear ratio, there are ways to estimate.
Just lift the back end off the ground and rotate the driveshaft by hand. Place some marks (tape, chalk, whatever) on the tire(s) and driveshaft and count revolutions. Go for a lot of revolutions, like 30, to get a decent estimate. If you have a locker, you'll have both wheels spinning. If the diff is open, keep one tire on the ground and divide the number of tire revolutions by 2. Your gear ratio is just the driveshaft revolutions divided by the tire revolutions. Then look for the standard ratio closest to that number.
Or you can use an accurate tach, a GPS and the true tire diameter to do the math.