A couple of decades of looking after free range chickens.

More seriously...
The chickens ancestors the jungle fowl lay claim to approximately one acre of jungle per breeding pair according to the few studies there are on the subject.
Bear in mind the Jungle fowl are smaller and may only lay 20 eggs a year. Generally due to the diversity of the vegitaton jungle forage is likely to be of better quality than most cultivated land.
Todays appropriately chosen free range breeds may lay one hundred and fifty to two hundred eggs a year. That's a large increase in nutrition demand and consequently a larger area is likelyneeded to support them.
The tribes I looked after in Catalonia occupied roughly an acre per tribe and as a new tribe became established their territory increased by an about an acre. These tribes did get fed commercial feed twice a day and in the spring and summer months the impact on how much commercial feed they consumed was roughly measurable.
Differing keeping arrangements will have an impact on these estimated areas even with free range chickens (technically yours are not free range if they are fenced)
So, as an estimate to make a noticable impact on commercial feed consumption I think half an acre per breeding pair is a reasonable estimate.