What size of a button can a reasonably fat finger comfortably click?

Say my button is square shaped, in a website, and I don't want to cause inconvenience for users with big fingers (and also older people and those who forgot their glasses and aren't precise at hitting the spot).

My guess is 40 x 40 pixels is a good click area, but won't it be too small on those new full HD phone screens? I have an older phone myself so I can't try it out :X

Perhaps someone has a good rule of "fat thumb" they use for these kind of issues?