I just set the four posts for my new coop in concrete the other week, the holes were about 8-10" in diameter, and about 22" deep with a treated 4x4 post set in them.
One thing I will say though is you WILL use more concrete than you think you will. I ended up using FOUR 80lb bags plus one more 40lb bag of Quikrete from Lowes. I had to get the fourth 80lb bag and that 40lb bag after I ran through the first three 80lb bags so fast.
What kind of soil do you have? If you have sand, it can be packed back pretty tight without much need for concrete provided you get the legs deep enough. If you have red hard clay that comes out in chunks such as myself, you are better off putting concrete back in the hole. There is no way to properly pack the chunks back into the hole around the post firmly enough to get a good bite. For me to properly set a post and for it to hold in my soil I have to dig the hole 2 1/2 times the size of the post that I'm wanting to set, then fill with concrete.
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I've set fence posts in clay by pouring water in the hole first, and then adding the clay to make mud that drys as hard as a brick
I wish I had that kind of clay, unfortunately I don't. It doesn't absorb water to break down at all. I guess that's why we now have to have these elaborate septic systems, so the moisture evaporates instead of soaking into the ground. When I did the 6 ground rods for my electric fence, I started the rods by digging a 12" deep hole. I drove the rods as far as I could and then filled the holes with water. The next morning the holes were still full all the way to the top as I left them the day before. It took me a week to finally get them all in.
I told the DW if we ever move, I'll be checking the ground. No more red clay for me...LOL.