There are apps to measure your battery endurance and to optimize it, but to check the battery itself, you'll need to take it to an Apple store and have them test it. If it's faulty, they may replace it on the spot.
On standby, mine gets minimal battery drainage - maybe 1% in a day. When I'm using it constantly with WiFi or cell, I can usually get 5-6 hours before the battery gets down to the warning levels. I've had it since shortly after the release date, so it's not new either. If yours is getting less, I'd go through the settings to make sure you don't have anything unnecessary running, extend your email fetch intervals or change them to manual, etc. If that doesn't help, I'd take it in and get it checked.