The general advice given around here is 4 square feet per chicken in the coop AND 10 square feet per chicken in the run.
But this also depends on whether they will spend all winter practically inside their coop because of heavy snow. Or if you free range them daily year round and just close them up at night in the coop (you might be able to squeeze more in in that case).
Generally speaking they REALLY appreciate more run space.
If you are buying the materials to build it, it costs only a little more to build 8x8, which gives you more room for chickens as well as room to store feed and supplies, and room to move around inside. Roosts, nests, etc. take a lot of room -- this gives the chicken more real space, and you can usually more than double the number of chickens.
If you never have conditions where they'll want to stay indoors most of the day (or, only a day or two per year), then really the main thing that matters in terms of indoor space is just having enough linear roost space for them. Depending on your coop design and setup, that could be 16+ chickens in a 4x8 house. I am not necessarily suggesting you DO that, of course -- and sanitation becomes MUCH more work than with fewer chickens -- but, I mean, if they are GENUINELY not going to hang out in there during the daytime, square footage is not the main issue.
(Mind, unless they have large areas of fairly deep shade that they can spend their summer afternoons in, they MAY want to be spending time in your coop, in which case square footage is back to mattering, as is ventilation in a big way)