You can do this more or less auto-magically using a chain of polygon boolean operations like intersection and union and preserving the original polygon IDs and creating a supplementary ID for each stage of the calculation for the final calculation. Conceivably, a buffer could have overlap with multiple protected areas, or none, so one needs to consider the edge cases. Each stage will require some creative table joins. In end, you end up with a table of buffer IDs with a one-to-many relationship to a table of protected area fragment IDs for each buffer and their areas related to that buffer. I'd use the qGIS model builder to progressively refine the process from the simplest to more complicated cases. For instance you may want to union protected areas at some stage if they overlap. This is a vast oversimplification based on the limited information in you description, and the graphic is only an simple example on how to think through the various cases you might encounter.

You can use intersect tool in ArcGIS to find the Buffers-Areas overlap with other Polygon-Shapefiles (e.g. Protected Areas, Military Areas). Once you find the intersection polygons you can calculate the area using calculate geometry. After that, you can add one field, like %occupied. And then you can add an expression to calculate the percentage by giving the area of the new polygon obtained from the intersection result and the existing total area of Protected Areas or Military Areas.

Thank you both for your answers. They brought me on the right track :).

In the end i first used the Intersect Tool for Vector Layers and then Used the Dissolve Tool (dissolving the different features by the Buffers IDs) to get one Polygon per Buffer each with the original ID of the Buffer. Then I calculated the Are with the aid of the field calculator and finally Joined the Area-column back to the original Buffer Layer using the ID i always had to preserve.

I still used QGIS.

Greetings :)

I think the software used should not create problems. Whether using ArcGIS or QGIS, the concept is the same.