I am planning to buy a new set of rims for my British racing green 2010 MINI Hatch John Cooper Works. What is the ideal size of tires that can accommodate this 16-inch rims like this chrome, 5-spoke American Racing AR883 Maverick rims? Or should I go for a smaller rim size?

A Mini will not take 16" wheels!

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DID I MENTION THAT I AM THE BEST SUPPLIER FOR MINI ELECTRICAL PARTS AND REPAIRS?
"Let us remove your "SHORTS"

His 2010 model will.

16” is a standard tyre size for that car- have you checked what’s on the tyre placard?

Oh ... A BIG Mini.

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DID I MENTION THAT I AM THE BEST SUPPLIER FOR MINI ELECTRICAL PARTS AND REPAIRS?
"Let us remove your "SHORTS"

A big car that is a mini in name only.
Only BMW knows what they were thinking!

Try this online calculator:

https://tiresize.com/tyre-size-calculator/

Plug in your original tyre size, hit 'calculate' and then on the rhs click on 'alternate sizes' - it will give you alternate 16" tyres with similar overall rolling diameter.

Just be careful with offset etc and clearance to your suspension, brakes etc.

Also worth mentioning looking into whether your insurance will be valid, have heard stories of insurers denying claims if tyres are fitted to car that aren't listed on the tyre size placard. This may just be an urban legend though!

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Dave - 64 Nurburg White Morris 850 & 67 Morris Mini Deluxe (Bro's Car)
Previous Rides - 62 Morris 850 (Sold '03 - Now 'Lulu-62') & 76 Clubman S (Sold '99 - SFW-863)
+ Too many other classics