Despite the number of answers "confirming" no, I'm going to provide some outside sources that indeed show you're correct, or at least in some situations you can be - although it's not to discredit the points made, and the difference in reality is negligible, in either direction.
There are several factors that affect your gas mileage based on how full your gas tank is. This includes, but not limited to:
- Size of the tank
- Shape of the tank
- Ambient temperature
See here, specifically point 2.:
- Gas Mileage
Some will argue that because the gas tank is lighter when its low, a low tank will give the car more fuel efficiency. A
lighter load does require less gasoline, but the weight of a full fuel
tank is not significant. A gallon of gasoline weighs only 6.3 lbs.
(for reference milk weighs 8.6 lbs. per gallon), so even in most large
vehicles the total weight of a full tank is under 250 lbs. Your car
may actually be less efficient when the tank is near-empty, as more
air in the tank can increase fuel evaporation.
And also this Quora answer:
In theory yes but, in practice it could actual hurt your mileage.
The reason is that the fuel will slosh and can get into a rhythm that
actual makes your engine work harder. Ask any trucker or farmer that
hauls liquid, a full tank is easier to move than a partly full tank
that is sloshing.
I'm not going to go into the opposite point as it's been well discussed, and certainly carrying less weight does increase your gas mileage. But compared to the weight of a car, a half tank of gas is well... effectively nothing. Just like the loss from evaporation or the fuel sloshing about is effectively nothing.
I think the important thing is that each of these differences, whether in favor of better gas mileage with a full tank of a half tank, are negligible
It's kind of like driving around looking for a better price on gas, you'll waste enough gas looking you won't save any money - you're better off putting your attention elsewhere.
The first link I provided gives other reasons it is beneficial to keep a full tank, and I typically fall into this line of thinking, but again, in general it's not worth the concern either way. Just don't hit empty.