For full sized chicken breeds the normal recommendation is a minimum of 12” cubed. They will use some smaller areas, especially if they want to hide a nest, but if you are building, 12” minimum. I made mine 16” cubed, width x depth x height.
Since your studs are 16”, it certainly makes sense to make them 16” wide, which is what I think you are planning. For the other dimensions anything 12” or over will work. A word of caution. I like a lip across the bottom maybe 4” to 5” high to hold the bedding and eggs in while they are scratching around in there with about an 8” opening above that for the hen to get into the nest. I’ve had them use a 6” height opening but that was a bit tight. So pay attention to your framing to make sure you leave enough of an opening height to accommodate this. That’s how I wound up with a 6” opening height for them when I had to raise the lip to keep them from scratching the eggs out.
