2006 Battery terminal bolt size

I bought a generic/standard battery bolts with square nuts at AutoZone but they were too big to go through the terminal holes on my 2006.

Browsing RockAuto, it seems like there are two common sizes, 5/16" and 1/4" but nothing metric (at least on that site). Could it be that I was trying 5/16" and I need 1/4" or do I need to actually go to a dealership to get this seemingly very trivial part?

 

Try using a regular 1/4-20 bolt to check size. It might be a 6 mm bolt.....

 

It should be an M6. I've never measured it but it uses a nut that's 10mm across the flats which is standard for M6