I held them up over the 11-12 spiderman slippers I got my grandson and they look to me that this is the perfect size. they sit in the sole with less than an inch to streatch to fit. I also looked at a couple different conversion charts and it appears that it your grandson would fit in the range of this size sock. The medium child sock like this should fit around size Child 11 to around a youth 2. Both charts are different but that is about the range of the medium.
I am trying to find out for you- I got some for my 5 year old grandson who is size 12 in shoes and for my 7 year old grandson who's foot isn't too much bigger than that. I am givng them both this size for Christmas.