A rule of thumb given on here are that the nests should each be a minimum of 12" x 12" x 12". If your nests are this size you need one nest for every four hens. Larger nests will hold more hens. Mine are 16" x 16" x 16" and I have no problems with 5 hens per nest. Some people use what are called community nests. If built right a community nest 2' x 4' can supposedly handle 24 hens but these are just for flocks that are for only laying eggs. They are not suitable if you want a broody hen to hatch eggs. Or you can build a roll-away nest. This is where the eggs roll out of the nest to a collection area that the chickens cannot get to, very useful if you have an egg-eater or are collecting a lot of eggs commercially. There is no one rule for size or how many, it kind of depends on what you are using the nests for. Typically you will find most of your eggs in just a few nests, they don't get used evenly. They seem to like to lay in the same nests. Still it's better to err by providing too many than too few.
My only rule for how high the nests should be is that they are lower than the roosts. Chickens tend to sleep in the highest spot available. If your roosts are higher than nests and you have enough roosts they usually don't sleep in nests. They poop while they sleep, not a good thing for clean eggs if they sleep in nests.
Some people put the nests on the floor. Set a milk crate or box down, fill it with bedding, fix it so the chickens won't turn it over when they perch on the side, and they are good to go. Other people put the nests high enough that they don't have to bend over to gather eggs, helpful if you have a bad back. Mine are in between. My suggestion is to make it convenient for you. People tend to care about height a lot more than the chickens do.
You need enough of a lip around the bottom of the nest to hold the bedding in. They tend to scratch when adjusting the bedding before they lay. If the lip is too low they can scratch bedding, fake eggs, or real egg out.
I've had full sized fowl hens (not bantams) use a nest with an opening height of 6" when I had to raise a lip to stop them from scratching stuff out. That's fairly tight but they used it. I try to give hem an 8" high and 8" wide opening. That just looks better. And if it looks right it usually is.
Some people will tell you that the nest has to be dark for the hen to use it, going as far as putting curtains on the nests to make it dark. I've had hens use a cat litter bucket with an open top. Many people use milk crates with an open top. Not dark at all. They do tend to want to hide a nest but what makes a nest look hidden to a chicken may look pretty wide open to me. I think shadows on the coop floor can sometimes make them think the nest is hidden.
That cat litter bucket I used had a top opening of 7-1/2" x 11-1/2", well below the minimum of 12". Hens used it and laid in it fine, but one time I let a broody hen hatch chicks in it. That did not work out well. The first chicks that hatch often like to climb up on top of Mama while they are waiting on the late ones. She was sitting so close to the edge of that bucket that when the chicks fell off they missed the nest and fell about four feet to the floor. Four different times I picked up a chick and put it back in the nest with Mama. They were not hurt falling four feet, by the way. But I retired that nest after the hatch was over. If the nest had been 12" the hen would be unlikely to be that near an edge. I'm mentioning this to show that there are plenty of exceptions to any rule of thumb we mention on here. They will use nests smaller than the minimum I mentioned, but there may be other reasons those rules of thumb are here.
The reason I used 16" for my nests is that if you cut an 8' long 2x4 or a 4x8 sheet of plywood into 12' or 16" pieces it comes out even, no waste. My stud framing was 16" so that made building 16" nests easy. I like easy.
These old threads show how some of us have made nests. You can build them from scratch but people have used pieces of furniture, buckets, someone even used a kitchen sink. There are no rules where there is just one right answer. Lots of different things can work.
Nest boxes
http://www.backyardchickens.com/t/41108/show-us-your-nest-boxes-ingenous-design-post-it-here/220
Nest Boxes
http://www.backyardchickens.com/t/4...-your-creative-nesting-boxes/80#post_12395882
Opa’s Rollaway Nest Box
http://www.backyardchickens.com/forum/viewtopic.php?id=287684
Since people tend to like photos I'll show what I did for mine. That 2x4 above them is my juvenile roost which gives my juveniles a safe place to roost away from the adults on the main roosts. The juvenile roost was a late addition, higher than the nests to stop them from sleeping in the nests. The tops of my nests became a droppings board but it's so broken up it is not a good design.
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