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Well, the smallest possible would be the biggest you can possibly bring yourself to build it
More seriously, I really hate to see them with less than 10 sq ft per bird total, preferably more like 15 sq ft per bird or more. By total I mean coop plus run. So for example if your coop is, say, 4x10 (40 sq ft), then you'd want the run to be at ABSOLUTELY least 6x10, preferably a lot more like 10x10 (or the equivalent), and frankly more is better.
Have you considered, instead of actually tearing it all apart and rebuilding it 6' tall, instead leaving the 4' high walls there and then using a horse panel (or part thereof, or even just 2x4 mesh if the run is smallish or narrow) to make and ARCHED roof? It would save you a WHOLE LOT of work.
Good luck,
Pat
OMG . read where majority say 2 ft. square , SOME say 4 ft. and YOU NOW saying 15 ft. square ? COME ON , now that is UNREAL .
MY run is 12x20 and COOP is 8x12 . Chickens ONLY sleep and LAY in the coop and spend most of the time OUT in the run . Even heard where alot of chickens EVEN LAY AND SLEEP in the run area or even on top of the coop . SO GO FIGURE