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If your speedometer is not accurate, your odometer won't be accurate either. You don't need a gas gauge but you do need a working odometer.
What you do is fill the truck up and write the mileage down. Drive it around until you have less than 1/4 tank and fill it up. The distance you just drove divided by the amount of gas you just used is your mileage. If your odometer is off 25% then your mileage calculation will be too.
Actually all you need to do is watch the guide posts, they have the mile markers every mile and on straight 2 lane roads the other posts are usually 1/10th of a mile apart, very easy to do the math as long as you put the truck on 60mph and also time the mile then adjust for how much time it takes above or below a minute to go that mile.
I have found many mile markers to not quite be accurate.. I know some use GPS to do the job of speedo...
+1 on that. Mine is accurate and has been checked against a calibrated speedo and radar. If you have a GPS like a Garmin or similar, put it up in the truck and go for a drive. If you don't have one, borrow one. You should be able to see how far your speed is off pretty easily. That's also going to carry over to the odometer and your perceived mileage. If the speedometer has never been corrected for the larger tires, you're going to be reading slower on the speedometer than you're actually traveling and you're actual mileage on the truck is going to be off.
9.3 does not sound right for a diesel not towing anything. Forget about the gauge, its meaningless for this. What was the stock tire size? You can find it on the door jam sticker. The odometer correction can be calculated if you know the difference in revs per mile. Tirerack.com lists that number in the tire spec tables.
Isn't there a way to check/change the odometer calibration by holding in the trip odometer button at startup? I know on my truck if I hold in the button, turn on then start the truck, then release the button it gives me a code on the odometer. IIRC you have to know the distance per single tire rotation to recalibrate to the correct code. Someone please tell me I didn't dream this....
Otherwise, I'd go the GPS route. Run the truck at various speeds (say 30, 60, 75 mph) on the speedometer and compare the speed on the GPS. The difference should be a constant percentage - if not take the average. Use this difference to adjust your miles traveled. If your speedo reads fast, adjust your miles traveled down by that percentage and vice-versa.
You could do the same thing using mileposts but use a bunch of them in a row. Individual mileposts aren't too accurate but they average out to be dead on.
As for the mpg calculation - the only accurate way is miles traveled divided by gallons required to refill the tank (assuming you started full). Individual tanks could be off some so average a few to get a more accurate number. Keep a running total of miles driven (adjusted for the speedo error) and the total gallons burned.
Other than for maybe telling you your tank is empty - forget about using the gas gauge. They are useless for mileage calculations.