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I'm looking to replace the stock 16" steel wheels on my 2010 207cc 1.6VTi Automatic with some sexy mag alloys and low profile tyres, but this is the first time I've ever done this and I'm finding the different options confusing. I think I've got it but would like someone to confirm if you wouldn't mind :)

According to wheel-size.com, the stock wheels are 6jx16 ET27 with 195/55R16 rubber on them. Is it correct that a larger wheel will have a thinner tyre on it, so that the combined wheel & tyre radius remains the same as stock, to avoid mucking around with changing gearbox ratios? I'm looking at either 7Jx17 with 205/45 or 7Jx18 with 205/40. Does the offset mean that the wheel is a bit recessed to compensate for the increased tyre width (so they don't stick out)? Will a difference of a couple of mm offset from recommended matter much?

Good looking 7Jx17 or 7Jx18 with 4x108 are hard to find here in Western Australia. I've found a set I like the look of on eBay but they have to be shipped from Italy and the rubber put on locally, so I need to get this right before ordering. I've also got some aftermarket TPMS valves I grabbed off eBay, ready to be fitted.

I'm doing this not just for appearance, but also I like a tighter tyre sidewall as I corner quite aggressively, upgrading the springs and shocks is next on the shopping list. Any and all relevant help gratefully appreciated.
 

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I'm not so clued up when it comes to offsets, but I can help regarding tyre sizes.

So breaking up what the tyre size means, 195/55 16, 195 is the width of the tyre (mm), simple. 55 is the profile of the tyre, not 55mm, but 55% of the width and obviously 16 is wheel size in inches. So you need to work out the total wheel size which is 16" plus 55% of 195mm and go from there. I haven't time to work it out right now but will later if you or someone else doesn't beat me to it!
 

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So breaking up what the tyre size means, 195/55 16, 195 is the width of the tyre (mm), simple. 55 is the profile of the tyre, not 55mm, but 55% of the width and obviously 16 is wheel size in inches. So you need to work out the total wheel size which is 16" plus 55% of 195mm and go from there.
Minor addendum total overall diameter would be essentially rim diameter (16") + 2x 0.55x195mm (IE rim + two times the profile/sidewall height

Offset can be tricky depending on how much space there is on the stock setup both inwards to the suspension components and outwards to the wheel arch.
If you put on a 1" wider rim and keep the offset he same, it will extend 1/2" further both inwards and outwards.

As an aside, another term for offset is "ET" from the German
EinpressTiefe (push in depth) The number describes the distance the rear of the rim face (which comes into contact with the hub face) is moved (outward for positive numbers) compared to the centerline of the rim. Move that surface outwards of course mean the wheel needs to go/push 'deeper' 'into' the car before it contacts the hub.

Looking at wheel-size.com for a 2010 207 GTI it says
205/45R17 88V 7Jx17 ET26
225/40R17 88V 7.5Jx17 ET20
235/35ZR18 87W 8Jx18 ET15

So it looks like there's a bit more space outwards than inwards, as the offset decreases as width increases. 7.5" is of course ~12.5mm wider than 7", so will extend 6.25 mm further inward and outward. Decreasing the offset from 26 to 20 effectively negates the extension inward, instead pushing it another 6mm outward (+ the 6mm / 1/4" an unchanged offset would do).
 

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Minor addendum total overall diameter would be essentially rim diameter (16") + 2x 0.55x195mm (IE rim + two times the profile/sidewall height
Correct, sorry my mistake there.
 
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