iOS 8 brings many features to keep you in control. Among them is battery usage data. This lets you see what apps have been hogging your precious electrons and might give you a clue of why.
Tap Settings > General > Usage > Battery Usage. Wait a moment and the data should load. You can toggle between data for the last day or the last week. If you just updated to iOS 8 nothing will show because the data has only started to get collected. Wait a few days and try again.
Some apps will show that the battery usage is due to background activity or from a low cellular signal, which can also drain your battery as your phone tries desperately to communicate with the outside world.
This isn’t going to necessarily pinpoint the precise cause of your problem, but if you have a program that is using more power than you expect you could try turning off background app refresh for that app (Settings > General > Background App Refresh). You could also try deleting the program and reinstalling it. Or maybe find a less power-hungry alternative.
Looking at my screenshot I’m not sure why YouTube is using up 10 percent of my power when I only did a couple of searches on it last night. It says something about background activity. Don’t know why YouTube would ever need to run when I’m not actively using it so I’m going to go revoke its background app refresh permission right now. Waze makes sense to leave background on. Every time I switch to a phone call or summon Siri while I’m driving I want my navigation to continue.