IPad Battery replacement criteria under warranty, no applecare
Yes, the warranty covers battery failure. 

The batteries capacity can be measured in mAh.
If Apple sells it with 1000mAh, then 500 would mean 50% (example numbers). I'm not sure at what percentage Apple considers a battery failure but I'm strongly assuming 50% within a year is considered a warranty case. 

Call AppleCare or take it to a store. They will give you a URL to enter in Safari (something like diag://12345)
That will send the test results to Apple (including battery capacity) and they'll tell you your options to get your battery swapped. 

There is no official way to check your battery capacity yourself (there are possibilities with jailbroken devices AFAIK).