[AT&T, Rogers, Bell, Telus Samsung Galaxy S III] electech13:
What you reported is definitely "the average". Most actually only get a day, if they're lucky of moderate use and have to plug in before sleep every evening and get going on charge in morning. So its more like 15 hours actually. And your 31 max is very common high end for people who've stretched it out.

I'm not sure if you're stock rom or not and if rooted either but that makes a big difference.

I'm rooted ( and would ALWAYS RECOMMEND ROOT FOR EVERYONE EVEN UF NOT FLASHING ANY ROMS AND STAYING ON STOCK. The ability to have full control is important.

Changing kernels and more importantly, undervolting, will give you that longer life you're looking for.

I'm currently on KyanROM with either Ktoonez or Faux kernel (heavily tweaking and testing both) and have this phone beautifully undervolted to exceptionally low and very stable mv numbers! Thus getting me that lovely 36-45hour average (you mentioned you saw posted elsewhere - yes it is possible and many are doing it). I basically only need to plug in every OTHER EVENING or night between 6pm and midnight depending on usage and I'm a moderate to heavy user (with a lovely 3-5 hours of screen time as well) AND I also have my phone overclocked to 1.8Ghz! Surprisingly, the oc doesn't make much battery life impact at all because the phone isn't constantly having to run at high levels, only in short spurts. Actually, due to rooting and kernel change I'm able to have my phone run as low as 192Mhz during much of its general activity and deep sleep ( which I get a ton of as my phone basically always goes into it when the screen goes off). This saves me A LOT of battery life.

I also use LTE, which is actually one of the biggest if not the largest battery hog, next to screen time of course. But with that being said I only use it when needed and have it turned off when not in use.

As for my peak I was able to squeeeeeze out 87 hours once, on my stock battery BUT that was with some abnormal(for me) measures that really help conservation. Ie, no LTE, under clocked to 1.2Ghz for good part of the three days, much less then normal screen time over the period of which I used it at lowest level with even further reduction via screen filter, I actually used airplane mode during my three overnight sleeps (which I seldom use but if you can hack it, do it! It can really save battery overnight. My current setup basically SIPS MY BATTERY AT 1% EVERY 3.5-4 HOURS OVERNIGHT WHEN IN AIRPLANE MODE), mobile data was off for most of time but did use my wifi at normal level (wifi uses less especially if good signal with few reconnects/scans), used my typical low UV numbers, kept my notification updates/syncs/wakelocks to a minimum and lastly kept my memory virtually clear if unnecessary background apps.

Doing ALL of this allowed me to get OVER THREE DAYS BATTERY LIFE. But keep in mind I seldom do many of these battery saving tips on a regular basis but some do and if you can, they WILL work to extend your life substantially!

To wrap up (this long winded post/reply) I'll give you my general UV mv range numbers and the typical everyday simple battery saving methods I use.

1.My voltage at lowest clock of 192mhz=800mv with gradual (smooth and almost linear curve) increase up to a mere 1200mv at a whopping 1.890Ghz clock.

I use NOOP scheduler with ONDEMAND governor most of the time, sometimes SmartassV2.

My screen off and deep sleep use this lowest 192 clock speed and with no wakeup lag.

2. I use my screen at 0% brightness most of the time (except when outside or in high lighting environment). I use the brighrness widget app to control this as it is easier and works better then stock settings. I actually even further reduce my brightness with Scree Filter App. That app is awesome and often use it solely for brightness control because it has full control and can dim it to basically full black if wanted. Which is MUXH lower then stock control. Fyi I use my phone a LOT more at night or in dark environment thus allowing me to dim screen HEAVILY yet it still is actually plenty bright with ample contrast in dark environments to do everything. This saves on my battery HUGE!

3. I use LTE when needed and GSM/HSPA+ when not. Seldom turn of mobile data altogether. I do turn off wifi when out and only using mobile data.

4. I use Screebl app to have screen turn off when not in use. Its great liitle app. Basically let's you turn down screen timeout to 15 seconds or less so screen is never unnecessarily on but it always stays on when in use due to the accelerometer and it knows when the screen is not flat on table! Its very annoying when browsing or doing stuff where screen isn't touched for long periods and the screen goes to sleep! But this stops that! So its always on when upright or in use and when phone down it turns off immediately.

5. Very important step and can take some time and research but making sure to keep partial wakelocks and apps keeping device awake to a bare minimum! DEEP SLEEP IS VERY IMPORTANT TO SAVE BATTERY! You basically want it to go into that every time your screen goes off and to stay in it uninterrupted for as long as possible. And many users phones are NOT making it into deep sleep due to partial wakelocks and they don't even know it or how to fix it. Not getting deep sleep can unnecessarily kill your battery!

I use a few tools here: Better Battery Stats/GSAM Battery Monitor/Battery Monitor Widget from within System Tuner Pro (which is my also my main and highly recommended tuner app for CPU oc/uc and UV,etc.).

These apps really help to determine what, if any, apps are causing partial wakelocks ( displaying in wake number amounts and overall wake time) allowing you to determine what to do to fix the problem and let the phone gets as much battery saving deep sleep as possible.

6.I'm not big on auto app killers and actually recommend against them as Android ICS does this already very effectively but do keep in mind that the more active background memory that is used, the more battery the battery is drained. So I personally kill unnecessary apps myself from the background whenever possible to save a little battery here and there. Using the apps listed above in #5 can really help to detect a nasty background app or service that is quite possibly unknowingly using a ton of CPU and/or memory, thus draining more battery and also often just slowing down your phone!

7. For those who can use it Airplane Mode is a big saver! Try overnights if wanted as long as missing notifications, emails, calls, updates, etc is alright for you. I seldom use it but it does help.

8. I almost never use my Bluetooth and GPS but when I do that is the ONLY time they are on. They get turned off immediately and really be careful with the GPS in particular because you might be surprised how many things on your phone will use it in the background, sucking your battery!

9. Be careful with sound and vibration levels. Haptic feedback too. I don't do much here but its anotherctip nonetheless.

10. Lastly is treating and charging your battery right! I found an amazing site linked down below in a couple of articles that really explains these batteries and how they work in a very in depth technical level this is still not too hard to follow. Aside from the two links I posted check out the others on the left menu as there is a ton of useful and educational info!

http://batteryuniversity.com/learn/article/how_to_increase_the_runtime_of_your_wireless_device

http://batteryuniversity.com/learn/article/how_to_prolong_lithium_based_batteries

OK I've rambled on waaay too long here. Maybe I'll take this and post a battery savings tips thread with it lol. "10 points"!

Btw I've just received both my 3300mAh and 4400mAh capacity batteries. So I have much testing to do on those too and I plan on reporting back on them as well. Also with screenshots for data and proof...I can and will also post screenshots for all of the numbers and stats I've posted here today with my personal phone/battery accomplishments.

Hope this helps some of you out there because yes this phone can be known for terrible battery life but it CAN be tweaked to SUBSTANTIALLY IMPROVE that life to high standards and keep up with the best of them!

On Stock battery - Kyan Rom/Ktoonez kernel (at this moment)