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A larger overall tire height (not just RIM diameter) will lower the RPM needed to maintain a speed, so it will improve your gas mileage. It will however make your speedometer and odometer read incorrectly, so those will have to be adjusted (this usually requires changing a small gear on the transmission).

Wider tires will reduce your gas mileage, because the added width adds friction between the tire & the road. Good for handling, bad for mileage.

Going up in rim size (like say from 15" to 17") will reduce MPG because the larger rims will be heavier, and will move the weight further out from the hub. Also lower-profile tires have to be built heftier to compensate for their shorter sidewall which adds weight out near to the edge of the tire. Rotational weight (tires, rims, brakes rotors, etc.) count for approximately four times as much weight as vehicle weight. So adding 10 pounds on the wheels, is like adding 40 pounds in the car, and added weight reduces MPG.

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Q: If you increase tire height and width will gas mileage measure the same because there has been approx 30 less mpg than before?
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