Sadly its a well known issue, the problem is not the battery, its the charger, in many units they sent out cheap chargers that are good typically for most cell phones but for the s4 the power it uses is larger than the charger can handle by default, and this is an unintentional mistake that I will tell you how to fix very shortly.
1. the easiest fix is to get a charger self sufficient enough to maintain the charge. The ones that can do this is the 5 pin data and charging, usb chargers, just connect the usb chargers into the wall to usb charger that came with the phone. The 5 pin chargers are more capable then the 4 pin that came with your phone. To get these either look for a charger that is advertised for data transfer as well as charging at usb 2.0 to 3.0 speeds, or go with these 3 charging companies I have found that work, either the most expensive and most durable for 25 dollars at radioshack for ifrogz, or i-sound about 8 dollars at tj-maxx (oddly not at marshals). These 2 are the best I have found.
2. fix the freaking reason why the heck the phone is using so much power. These chargers are great because even if you find them actually less necessary after you fix step 2, you will find that they can totally charge the phone up 100% in about 1:20 hours. The phone was tested before it was sent to the reseller, but some of the resellers have bad firmwares and is causing google maps to run 100% of the time. Do a factory reset, sadly this means you will loose your apps and the problem usually is fixed. This should be done if you are seeing in your battery menu google maps always running at 10% or more of your battery and never closing. Even with the chargers I recommended that will be able to charge it with this bug. The phone will drain withing 10 hours on idle doing nothing to 0 and in 5 hours in hard usages. Refreshing to factory stock will fix this glitch. The phone should by 69 hours idle, and about 10 hours of hard gaming use. Its not the most efficient piece of hardware but its more efficient then what a large chunk of what people are getting out of it right now. I am sorry for your pain, I delt with it too just a couple days ago as well.