BTW, I'm 6'3" tall and didn't want to be hunched over in a 6' tall run. I came up with the formula to figure out a width for mine. It's not exact unless you have a perfect half circle on top, but it is so close, within a half inch you can use it anyway.
If your coop were say 7' wide and the sides were perpendicular to the ground and parallel to each other until the half circle began, 7' would be the diameter of that circle xPi (3.14) = 21.98'. Call that 22', but you are only using half the circle, 22' x 1/2 = 11'. If you take the 11' off of the 16' panel that you started with 16 ' - 11' = 5', you have five foot left, but you have two sides, 5' X 1/2 = 2.5', you have 2.5' feet left for each of parallel parts of the walls. So 2.5' up to the center of the circle plus the radius of a 7' diameter circle is 3.5' comes to 6'. But there is more. I used 2" x 6" skids on bottom, but temporarily tacked 2" x 4" (which are really 1 1/2" x 3 1/2" to them to rest the panels on before attaching to; 1. give me a level line that the panels could rest on while being stapled to the 2x6. 2. to get me above the 2x4s that I used for cross members, and 3. to give me that extra 3 1/2" in head room, or 6'3 1/2" total.
After rethinking it, I found that 8' wide came to 25.14, or a 12.57 circumference on my half circle (12.6' off of 16' leaves 3.4' and half of that is 1.7' or 1 3/4' = 21") The new radius, plus the 21", plus the 3 1/2" on the skids came to 6'1/2". I was still ducking when it was 6'3 1/2" unless I was smack dab dead center anyway, and after bumping my head enough when I wasn't, I found myself ducking out of habit anyway, so I took it all back to 8' in the end. If I'm going to duck anyway, why give up that foot of width, or in my 3 panel run, 12.5 '².
Maybe I wouldn't be ducking in a 6' wide run, that comes to 6'6 1/2", but only in the center, yet would cost me over 25'² of run. I'll duck.
For those of you that are not so tall, and or willing to duck even more, I get 9' wide = about 5'9 1/2 tall, and 10' wide = about 5'4" tall. These figures are all with the same 3 1/2" high starting point for the wire.
After a few inches beyond 10' wide you'll just come to a perfect half circle that's barely over 5', and from there on you'd need a new formula that considered slicing a circle. I haven't figured that one out yet. But I had considered side walls. 2' side walls ten feet apart with a half circle on top would get you back to 7' tall again. Something to think about, like a giant Suscovitch tractor with a cattle panel hoop coop on top. You'd have to beef it up and pull it with a tractor, but it'd work out in a field, and if you're going for the tractor anyway, you mind as well make it longer too.