With some simple math, anyone can determine your gear ratio without removing axle covers. You will need to know a bit about fraction and decimal conversion, but I'll put up some info here to make that easy for you. Most of are aware of the basics without even thinking about it. Examples, being 1/4 is .25, 1/2 is .50 and 3/4 is .75.
On to the good stuff. First thing you want to do is figure out if you have a locker, spool, some Limited Slip Diffs (LSD) or locked axles as in Lincoln Locked or welded spider gears making the open diff a locked axle OR, if you have an open differential or Limited Slip Diff or Locking Diff that doesn't lock the axles until a predetermined set of events happens to make them lock up.
This is easy to do. FIRST chock the front wheels in both front of the tire and rear of tires so it doesn't roll since your E brake goes to the rear wheels. Jack up the rear end with both wheels off the ground. I usually use a floor jack in the center of the axle. With both rear wheels off the ground. Spin one wheel. If the other wheel spins in opposite directions, then you likely have an Open differential without a locker or LSD, but G80 Locking Diff does also spin in opposite directions, so you could still have locking differential. That doesn't matter for figuring gear ratio though. Bottom line here, you're trying to determine if the wheels spin in opposite directions, or Not. If you go to spin the one wheel, and it doesn't turn at all, then you'll need to put the transmission in Neutral, and this is likely going to mean you have a locker, good LSD unit or welded spider gears. After the trans in N, spin the one wheel, and it's likely to have both rear wheels spinning in the same direction.
It's important to know this, if the wheels spin in opposite direction or if they spin the same direction. If they spin the same direction, then it's even easier to determine the gear ratio. If they spin in opposite directions, then you have another step of multiplication to do. So lets do the easy one first, and assume the wheels spin in the same direction.
I use the valve stem on the tire as marker and start my wheel spin count at 12, 3, 6 or 9 o'clock position. Whichever position I have the pinion yoke or U joint either straight across or straight up and down. It just makes it easier for an accurate count. Then you're off. Make 1 full tire spin by hand and count how many times the driveshaft, or the pinion yoke turns. If the driveshaft spins:
Wheels Spin in the SAME direction.
A hair over 2 1/2 times or 2.5 times, then safe to say ratio is 2.56:1
A hair under 2 3/4 times or 2.75 times, then safe to say ratio is 2.73:1
A bit over 3 times, then safe to say ratio is 3.08 or 3.07:1
A hair over 3 1/2 or 3.5 times, = 3.54 or 3.55:1
A hair under 3 1/2 or 3.5 times, = 3.42:1
A hair under 3 3/4 or 3.75 times = 3.73:1
A bit over 4 times = 4.10 or 4.11:1
A hair over 4 1/2 or 4.5 times = 4.56 or 4.57:1
A bit under 5 times = 4.88:1
A bit over 5 times = 5.13:1
You should have this by now, so that's as far as I'm going and anything else is very uncommon anyway in light duty trucks and cars for sure.
Now, if the wheels spin in opposite direction the procedure is a bit different.
You must put 1 wheel back on the ground so it stays stationary and you can get an accurate count. This is because if the wheel is moving, that means the spider gear to the that other axle shaft is moving and you don't know exactly how much and it makes your count inaccurate. So with just one wheel in the air, transmission in Neutral so that the driveshaft is able to spin, then count the pinion yoke spins to 1 full tire revolution. Now here's the difference and the added step. Take the # of spins and multiply it by 2 and that is your gear ratio. The reason you have to multiply it by 2, is because the distance you are moving the wheel, the spider gears are spinning backwards on the other stationary axle shaft gear, cutting your pinion yoke turns in half. So if you pinion yoke spins:
Wheels Spin in the OPPOSITE direction.
A hair over 1 1/4 times or 1.25 times, x2 then safe to say ratio is 2.56:1
A bit over 1 1/3 times or 1.33 times, x2 then safe to say ratio is 2.73:1
A bit over 1 1/2 or 1.5 times, x2 the safe to say ratio is 3.08 or 3.07:1
A hair over 1 3/4 or 1.75 times, x2 = 3.54 or 3.55:1
A bit under 1 3/4 or 1.75 times, x2 = 3.42:1
A heavy bit under 2 times x2 times = 3.73:1
A bit over 2 times x2= 4.10 or 4.11:1
A hair over 2 1/4 or 2.25 times x2= 4.56 or 4.57:1
A bit under 2 1/2 or 2.5 times x2 = 4.88:1
A bit over 2 1/2 or 2.5 times x2 = 5.13:1
And that's how it's done. Now noone should need to remove their diff cover, unless you're just wanting to do a differential oil change, to calculate your gear ratio. Which, if you don't know the history of your truck, it's not a bad idea to change the gear oil, and identify which carrier you might have when the cover is off. Keep in mind, some units require special oils like synthetic, or synthetic blend, some require GL4, some GL5, and some require LSD additive, so make sure you get a good ID on your carrier type if it appears to be a Locker or LSD.
Your poor transmission is working it's ass off. I'd be keeping your eyes open for some 4.10 axles. Many times you can find a set of used axles drum to drum for about $200-$250. Finding 4.10's in half ton axles is pretty tough, but 3.73's are out there in half ton. 
