If you're having 100% or nearly 100% awake time, that's obviously going to kill your battery. Here's the easiest way (without installing any new apps) to see what's keeping your phone awake:
1. Go to "Phone".
2. Dial *#*#4636#*#* (you won't need to hit send).
3. In the menu that shows up, choose "Battery history".
4. In the first drop-down menu, choose "Partial wake usage" and wait ten seconds for it to load.
5. Top item in the resulting list is what's killing your battery.
If it's "Calendar" it means one of your sync accounts (Google, Exchange, Facebook) is stuck in an endless loop of trying to sync. Reboot usually fixes that, or you can go one-by-one and manually sync till you find the culprit.