iPhone6 shuts down with 31% battery reading.

iPhone 6, 65 GB iOS 8.4.1

Battery indicator says there is 31% battery life but my iphone 6 shuts down. If I plug it in to my computer to recharge with ITunes open it reads 1% battery when it comes back on. the only problem is it goes into a loop and just keeps shutting down and restarting. I couldn't shut the phone off and let it charge in the off position connected to the computer because every time I turned it off it just came back on like it does when you plug in the charger. It will not recharge the battery enough to start the phone. I can plug the phone into my computer if the phone has not shut down and it works fine.

If I plug it into the wall charger it reads 31% and will then recharge.

I Have tried shutting it off and letting it sit over night then turned it on in the morning. when it came back on it had a battery reading of 3%. I charged it for several hours just to make sure I had a full charge but when it got down to 31% it shut off again.

I have put it into recovery mode and reinstalled the software but that didn't fix the problem.