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So I bought 245/40 R19 tires...

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I decided to take the risk and buy them as they were 150$ each. They are new. They are the exact same Michelin MXM4 that come stock with the Model S...
http://www.tirerack.com/tires/tires...dewall=Blackwall&partnum=44VR9MXM4P&tab=Sizes

My Tesla is a 2013 S60 rwd.

What will happen if I install those 245 40 19 instead of the normal 245 45 19?

I need someone that knows exactly the answer... The diameter difference is 3.6%.

I heard Teslas wouldn't mind a 5% diameter difference. Is it true?

Please advise today if possible, because I need to install tires tomorrow.

Thanks a lot guys!
 
Assuming everything still clears the body work and brake assemblies, not much will happen. The circumference is slightly smaller to start with your proposed tire, so the car will be be effectively geared a bit lower. On conventional cars, that would throw the speedometer/odometer readings a bit off. In this case the slightly smaller tires would turn faster at a given speed, slightly over-reporting speed and miles. I don't know what the basis is for Tesla's speedometer/odometer setup, so I don't know how significant that slight change in circumference is.
I will also say that 0.05X245 is 12.25 mm or 0.48 inches or so. If you think about it, a tire's diameter and circumference is never perfect. That is, tires start out bigger when new, and easily wear down a quarter of an inch or more as they get older. That and normal variations in inflation pressure will increase/decrease circumference as well, even within the allowed tolerances for inflation pressure monitoring.

Tire experts, correct me by all means, but that doesn't seem to me to be much of a significant size difference that is being proposed.