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As long as the overall diameter of the tire remains the same then very little (trading a little extra wheel weight for a little less tire weight is a push). If you go wider or softer with the tire then that will go against your MPG.
If you go "bigger" (larger diameter) then that will reduce your mileage as your truck is programmed for the OEM circumference of the tire.
^ What he said. What you're referring to is the wheel size, not the tire size. Other than a little weight, changing the wheel size affects nothing, it's a change in tire size that will really affect the truck. What tire size do you have now?
For example, my '17 Sport came with 275/60/20s stock. When I bought it, it had some load range E 10 ply Cooper all terrains on it that were heavier than stock. So instead of the 19-22mpg my dad gets with his highway tread tires, I got about 17-19mpg. I just put some 35x11.50x20 Nitto all terrains on last week, so far I seem to have lost maybe 1mpg.
The reason I didn't lose more is because these Nitto Terra Grapplers are the lightest AT on the market. Going up in size and up in weight will decrease fuel mileage. It will also throw off your speedometer. If you don't want to deal with your speedo being off or getting the truck tuned to compensate and also don't want to lose fuel mileage, just make sure the 20" tires are roughly the same size as the 18s you have now. Below is a good tire size calculator I use all the time:
The best tire size calculator. Use our tire size calculator to find tire size specs and suggested tire sizes. Then check prices for all available tire sizes.
I went with the XL-rated Ridge Grapplers which were actually a little lighter than the C-rated "off-road" tires that came with my ORG package.
Bumping up to E-rated adds 10-15 lbs per tire, which is a lot of inertia. That takes a lot of extra gas to get that unsprung weight rolling...and keep it rolling.
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