I see some folks who question the car's calculated mpg. I seriously doubt if it is off by much at all, and it's likely to be as accurate as using the calculator method. If you calculate by "hand" are you sure your filling up the tank to the same level every time? Have you checked to see if the odometer is accurate?
The reality is that with the current electronics and information supplied on-line they very accurately measure how much fuel is being electronically metered to the engine. I'm sure there could be some variance, but it's very unlikely they are off by more than 1-2%. While I don't use a calculator, I frequently run the numbers in my head, and I've always done it. They aren't off by much.
2012 BMW 550 M-Sport
2012 Acura TL SH-AWD---Wife's car
2013 BMW 1600 GT---2011 Kawasaki Ninja 1000---2012 Ducati Panigale