Given what you've tested I would say the battery is very suspect! You should be getting around 8 hrs of simple Web browsing at best, heaver graphics will lower this. I get around 5 hrs on my laptop doing VPN connections which are more compute intensive.
Here's a few Apple T/N's that might help lengthen the run time:
* [https://support.apple.com/en-us/HT204054|About Mac notebook batteries]
* [https://www.apple.com/support/macbookpro/batteries_power/|Batteries & Power]
As additional reference: [http://www.everymac.com/systems/apple/macbook_pro/macbook-pro-unibody-faq/macbook-pro-early-2011-real-world-battery-life-test-results.html|EveryMac - Unibody MacBook Pro Q&A].
If you still can't get more out of this system I would recommend you get a replacement battery (a better quality one) as the start point.