Is my iPhone 6 battery faulty?

I just bought a 6, and I'm terribly disappointed. I'm literally dropping a percentage of battery per minute while I'm posting this question - I started on 39% and right now I'm on 28%.

I've switched off nearly everything - visual effects, location services, push mail, sending diagnostics to Apple... you name it. The standby is fine - if I do nothing with the phone, it sits on 100%. But God forbid I should browse the Web, check Facebook, or do anything else with the phone!

Is something wrong with the hardware, or are my expectations of this phone just too high?