I have to replace a toilet tank that has cracked down the entire side. What dimensions, and capacities to I need to know when finding a tank to fit the existing bowl?
It is possible to buy just the tank which matches your toilet. I have done just that when I smashed my tank trying to move the toilet to fix the seal. The model number was printed inside the tank and a little internet searching found the tank, with all the hardware in it, could be shipped to the hardware store right beside my house for about $80, which was about 1/3 of the price of the new toilet. Since the hardware was included, the repair was incredibly simple.
Try searching for any identifying information inside or outside the tank or bowl. If you can find something, don't be afraid to spend 20 minutes looking, you could save a bit of money.
This is usually impractical. An entire new toilet with matching parts is often going to cost less (and much more reliably fit and work together correctly) than sourcing a part for a specific older toilet.
While all of the other hardware that goes into a toilet is normally available as aftermarket parts, I have never seen tanks and bowls sold separately, so I'm guessing if you can get them that way at all it's going to be special order, and I would not be the least surprised to find it more than the cost of a whole new toilet. I'm not saying it never happens, but I've never seen it.
Throwing in my $0.02.. The decision of whether or not to replace the tank should be based on the toilet. If the toilet is old, then it would be better to replace it. Beginning in 1994, a new US government mandate stipulated that any toilet sold in the US has to be a low-flow toilet which uses no more than 1.6 gallons per flush (gpf). This was done to reduce the amount of water consumption in US households.
The new low-flow standard used half of the water of the old standard which was 3.2 gpf. Since the new toilets used less water, they didn't work quite as well. They would clog frequently and would also require several flushes to go down properly. Toilet manufacturers were flooded with complaints (pun intended), and they improved the designs so they would operate properly on 1.6 gpf.
As a general rule of thumb, if it was manufactured after the year 2000, then you are fine. The manufacture date as well as model number, etc. should be inside of the tank somewhere. If it was manufactured not too long ago, and it is a name brand, then chances are that you would be able to find a replacement tank. If it is older, and/or it isn't a name brand, then it may be better to replace the whole thing.