My car has 15" tires , the manuf. says I can also run 16" tires. I was just wondering if there is a difference in gas mileage if you are running 15" or 16" tires?

This is probably going to get no real definite answers for you. I bet this is an ongoing debate somewhere.

On one hand you can say that there are less revolutions needed with the 16 inch tire to go the same distance... which in theory would save gas. The counter argument to that would be that the bigger tire would have more weight and drag which would cause you to use more gas.

I would say if there happened to be a benefit one way or the other, it would be so minor that the extra cost of the wheels and tires wouldn't make it worthwhile.

Will it make a difference in gas mileage if I run a 15" or a 16" tire on my car. Manufacturer says either size can be used.

I would not bet against you odinn7... The debate goes on...

If you just put 16" on you will throw off your speedometer and odometer. You need to size the 16 to have the same circumference as the 15". No difference in mileage and tires for 16 are more expensive. .

The rim size will change but the rolling diameter won't be.
This correction is done with a change to the aspect ratio (height of sidewall).

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If this important feature isn't addressed when selecting tires, everything gets skewed. Not only will you alter the speedo and odometers, but the braking effort will be changed as will gear ratios and engine torque curves.

So, to answer your question: No, you will not likely see an increase in fuel economy due to the change in wheels. Any improvement would likely trace to the tire type and it's characteristic rolling resistance.
Clear as mud yet?