Concreting posts for patio. How deep and wide?

[paul.deitch]

I have an existing patio pergola which uses 14cm square posts 2.8 meters high and painted white. The posts sit in a square U form which is concreted in. The pergola is 6 m long and 4.2 m deep. Looks great and I want to extend it sideways another 4 m to completely cover the side of the house.
I didn't see them build it so I have no idea how deep you need to go for the supports and what dia hole I need to dig.

I am sure that somebody here has the experience to suggest a starting point. Thanks