Would a 225/45-17 on a 7 inch wide wheel be the same diameter as the same tire on a 9 inch wheel?

 

Yes, the height will be the same. Personally, I think stretching 225 around a 9" wide rim is a bit much though, unless you are racing it and want 0 sidewall flex. It will look a little funny on the road probably.

 

i was just using those sizes for an ezample. the set-up i am going for is 215/45-17 on a 17x7 and 245/40-17 on a 17x8, and according to the tire size calculator those tire sizes should be the same diameter. I just needed to know if the width of the rim would make a difference. thanks.

 

The tire diameter will change a bit, the sidewalls on one could be straight up but on the other they could be stretched out at an angle. Get your hands on a wheel and tire fitment guide, most tire shops should have one. Wheel size is also important for tire performance. If a wheel is too narrow or too wide, the sidewall won't work as it is intended, so you could lose steering feel or cornering grip.