99redsport: They came stock with all sorts of ratios, 3.27, 3.55, 3.73, and 4.10
Most common on a 4 door 4x4 Explorer is 3.73
With 32's you will want 4.10's or 4.56 depending on the trucks use.
GoosR:
$150 for a disc braked Explorer 8.8? I see you have a 98, it is AWD?
You see the Explorer after 95 has discs, most of them have limited slip year axles.
The V8's and others also have traction bars built onto the axle.
So if you want a bolt in replacement you have some research to do.
Again it is EASIER to get the ring and pinion and have it installed.
OR
You can find the right rear for your truck, no a Mustang, Ranger, or F-150 8.8 will not bolt in. The Explorer also has 31 spline axleshafts, anything else would be a down grade.
If you are going to swap the entire axle out then you will want to convert the new unit to spring over, you will want to replace the parking brake assembly, and at the very least the brake pads, if not full calipers, rotors, etc.
I find it very hard to believe a Explorer 8.8 with disc brakes and 4.10 gear ratio, limited slip will be $150 at a junk yard. That doesnt mean it doesnt happen, I have seen one from a 2001 sport with only a few hundered miles on it total be snatched up for $150 so anything is possible. However FYI this rear axle is a very popular upgrade for Jeep YJ's so the junk yard price has gone up with the demand.
Now I have been around for a while and I do all my own work, I have a 97 4 door 5.0L awd 8.8 31 spline disc braked 3.73 limited slip under my 88 BII. This required cutting off all the explorer style mounts, traction bars, etc. I then coverted the axle to spring over to match the BII leaf spacing and adjusted the pinion angle. I also had to fabricate a BII style sway bar using part from the Explorer, the BII and a Ranger. I also had to weld on BII style shock mounts.
I have since replaced the parking brake assembly, the ring and pinion, had the limited slip rebuilt for more grip, eliminated the stator ring for the ABS brakes, replaced the rotors, calipers, and pads, amongst other things.
Going to 4.10 will be a nice upgrade for you but if you plan to run 33" tires, chances are you will go bigger soon after so the 4.56 or 4.33 (2wd only) would be a better choice. These ratios were not available form the factory.
Ring and pinion gears along with install kits are cheap and labor is reasonable. Again I believe this is a much easier route then swapping out the entire rear axle. It is also cheaper in most cases.