I find that hand calculation and the computer are always fairly close. Both are an approximation anyway, with the computer probably closer since it is measuring how much fuel it ran through the injectors and how many miles the car has been driven.
With hand calculation it isn't any "more accurate" because you are assuming that when you fill up that you put exactly the same amount of fuel in each time. But temperature, pressure of the fuel pump, vapor in your tank, all affect how much you put in each time. The only thing you know for sure is how many miles you drove. You don't know if you filled up the tank to the same exact spot it was sitting at when you filled it last time though. So, it is still an approximation.
This afternoon for example the computer said I had used 10.21 gallons since the last fill up. But the pump only put 9.90 gallons in before it stopped. (I have an app on my phone that I use to track fill ups). So I likely used more gas than the pump would put in given the much hotter temp when I filled up this time and the vapor in the tank shutting the pump off. Which one was the more accurate reading - they were within tenths of each other.
2013 MCA Convertible, automatic - Revelare Designs cowl hood, Hellion single turbo.