The traditional space requirements for chickens was 4 square feet per bird. So for your 4 birds, a coop with INSIDE dimensions of 4' x 4' might work. However, chickens do better and are happier when given as much space as possible. If left in the coop all the time, I'd bump that up to 10 sf per bird. That also happens to be the space many suggest for the open runs. So closer to 6' x 6' would be suggested.
An aspect of chicken coop math that is seldom mentioned, if at all, is how much space expands simply by adding a foot or so on one side. For example 6' x 6' may not sound like it is much larger than 4' x 4', but the interior space increases 2.25X. An 8' x 8' coop may sound like it is only double a 4' x 4' coop, but it is actually 4X larger and nearly double that of a 6' x 6' coop. Also, for any given amount of exterior linear wall space, the closer to square it is the greater interior volume you can get from your limited materials.
The numbers used for most commercial coops are grossly misleading. They seem to be using the "cage free" standard used by commercial laying houses, which is around 1.5 SF per bird (which is about double what a batter cage house would be). But imagine keeping 10 birds in that 4' x 4' coop. That is just silly.
External runs help expand space and tend to be open air. But unless they are covered, they also tend to be messy and even more so if you live in wet climate.
