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If my current car came with 205/55R16 all-season tires, would it cause any problems to use my 185/65R15 winter tires that I didn't sell when I sold the old car?

Both sets of tires are mounted on matching rims, so the rims aren't a problem.

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It should not be a problem, the difference in diameter is -1.6% according to this web site (https://tiresize.com/) so your speedo will be off but only by a small amount, you will be doing 59 when it is actually showing 60 and that's about it. Also you manufacture might have included +1 and -1 size tire sizes on the side of the door you might want to check them out.

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    Also the correctness of the speedo will vary as the tires wear down anyway. – Ryan V. Bissell Oct 18 '16 at 4:15
  • If tires are smaller, they have to do more revs for the same speed. So the displayed speed is higher, not lower. – sweber Oct 18 '16 at 6:36
  • @sweber you are right, edited – method Oct 18 '16 at 6:42
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As mentioned in other answers, the difference in size is manageable. A good rule of thumb is to keep it under 3%, you are at 1.6%.

Bearing that in mind, the next time you are shopping for snow tires, if you want to keep your 15-inch rims, get tire size 205/60R15, it's only off your stock size by 0.8%.

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