[Peter_AUS]

If you change rim size up from 15 inch, the for each change in size, 16 inch, 17 inch up to 20 inch you change the tyre profile accordingly. There are a few sites that do the calculations for you based on current rim and tyre sizes to what you are looking at changing it to. I am thinking of putting my 16 inch rims with new tyres to suit on my wife's i30 from my iX35 and changing my rims and tyres to 19 inch. Just thought I would put that in the mix for everyone. It is possible to put 21 Inch rims on an i30 believe it or not. I was surprised as I rang Hyundai up and asked the question, as from memory when I bought my iX35 you could accessorize the rim/tyre choice, I stuck at standard. I think it was the same for the i30 back in 2011.

I don't think I'd like to try 21" rims on my i30, the wheels might fit but the tyres would literally be rubber band thickness first pothole you hit will write those rims off

[Dazzler]

.. and the other issue would be Insurance. Most insurers get narky if you go up more than 2 sizes from standard fitment.

[Surferdude]

CraigB and dazz are both right.
Ride quality would be seriously compromised. Most 18" and over passenger vehicle rims I have seen have at least one buckle per set by the time replacement tyres are needed. And 2 or 3 out of 4 is not uncommon. You spend forever chasing balance problems and uneven wear.
To expand on the insurance issues, don't just phone and ask if it's OK. You need it in writing. Otherwise, come claim time.......... Sorry.

[The Gonz]

Hmm ... I might crank out a tyre profile matching calculator to go with the fuel economy calculator lurking on this forum