would leaving my galaxy s4 charging over night do any kind of damage to the battery?

Some battery data for me today. I first drained the battery down to 15%(playing video 9am- 5:50pm) and then charged back to 100%(6-7pm), then kept the phone playing video while plugged in(after 8pm).

As you can see, normally battery temp is in the low 30 C range, charging the phone from 15% to 100% raises it to 40C+. However as phone's battery % pass 90% the charging slows down and battery temp drops back to low 30s. Keep the phone running while plugged in (90-100% battery) doesn't affect battery temp much if at all.

Since over-discharging & heat are the two biggest killer of Lithium ion battery, you are much better off leaving your phone plugged in when you can instead of letting it drain all day then recharge a large %.

Edit: added One last screenshot(9:55AM): my battery temp after leaving the phone plugged in overnight: As you can see the battery temp stays very cool(Ambient is 24C).

The only time my S4 battery goes to 40 degrees or higher is when it's on charge & kitkat decided to play up making my phone really hot & almost unresponsive. When that happens I have to turn my phone off & wait for it to cool down before turning it back on. Normally my battery goes to about 38% while charging.

Posted via Android Central App
 
Quit worrying about the battery. Plug it in before you go to bed an unplug it when you get up in the morning! There is a charger built into the phone and it takes care of the battery. It can not overcharge, can not over discharge and can not develop a memory effect!

If I use my S-4 a lot during the day I plug it in the car or on my desk just to be sure it has enough charge to make it to bedtime. Batteries usually outlast my phones doing this..
Lithium batteries do not like to be deep discharged. The built in circuit will cut the phone off before the battery is discharged too far!
 

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