OK - nobody panic.
How about charging from only 40% to a full 100% in 15 minutes. Yes - impossible. So - I've been there.
If you are rooted, join me in the All Things Root forum in this thread:
Otherwise - for stock phones, please read on.
All of the funny charging times is because your battery subsystem is out of calibration.
This happens from time to time, and it's especially common when there's some kind of kernel change - or major enough changes in apps / usage / habits. (And the phone automagically decides what's major - not us users.)
All of the observables being reported about charge percentages and times are based on a single data file - that is now a little out of whack - and that's what we call "out of calibration."
Not rooted, you can't erase that file and make it start over, so you have to nudge it along until it straightens itself out.
(In fact, if you simply do nothing the problem will eventually clear itself - but that will take way too long.)
Plan this to take a few nights -
So - run your phone until it says it's out of power and shuts itself off. Normally - we don't like doing that with LiIon batteries, but it seems that the built-in protection circuitry won't let anything bad happen and more importantly - when your phone says it's out of juice and shuts itself off - when you power it back up, it's going to say that it has more than zero battery.
Now - charge the phone to full, or as best you can, with the phone powered off.
Use normally, next day, run out of juice again.
Charge phone to full, or as best you can, with the phone powered on.
Report back if this is helping and where things seem to be stuck if not.
There are a small percentage of cases where it could be a bad battery and even smaller percentage where it could be the charging circuit - but my bet is on this being a simple calibration problem from the stuff being described.
Hope this helps!
PS - whenever you a thread self-reference with a mod thanks, that's a mod thanking for pointing at the suggested merge.