For us 6 ft tall. I am 5'4" and DH is 6'3". I tend the chickens, but if he needs to get in there for some reason he can.
Height is more for the human aspect of it I believe.
My chickens are welcome to every inch of space I can give them. They do enjoy standing on perches in the run and any time I bring in a chair they get on top of it.
At 4 and 1/2 ft tall you would end up ducking or knocking your head IMO.
I would not want to get knocked out in the chicken run. They might eat me.
Yep its about sq footage for the birds enjoyment but its also about height for the health of your back. Personally I think that building the area for the birds and yourself larger than you think you need to begin with is the best way to go. Good luck.
I have 2 coops and runs, my first coop is smaller, and the run is only 5', and it's covered with 1x2 welded wire, with a couple of 2x4's inbetween for support. I am 5'6, and you have no idea how many times I have had a goose egg on the top of my head! My other coop is larger, and we learned, so the run is 6'high and also covered. So much better, plus I have more room to put some roosts in the run, and still be low enough that nothing can injure a bird from the top.
If you want to keep your run clean, you have to go in there, if you have younger ones in the run, you have to go in there to put them to bed at night, until they learn. I feed mine in the coops, but in the summer I put extra pails of water in the runs, which for the most part I can fill with a hose, but every few days I have to go in, empty them and clean the crud out. I know that I am in my run alot more than I ever thought I would be. Having room for a chair in the run is nice also, especially if you don't free range, or like me, you can't free range often.
Ours is about 6' tall. DH used 4 x 4 posts set in the ground about 30" and then added to the top with 2 x 6 boards to make it that tall. I am adamant about not having to bend over while in there. Our new coop will be tall enough so I don't have to bend over (but dh will at the shortest end).