What is an area of control responsibility within an ARTCC or TRACON referred to as?

In the context of air traffic control, an area of control responsibility within an ARTCC (Air Route Traffic Control Center) or TRACON (Terminal Radar Approach Control) is referred to as a sector. A sector is a defined airspace region where air traffic controllers are responsible for managing the flow of air traffic, ensuring safety and efficiency by coordinating aircraft movements within that specific area. Each sector has its own set of airspace boundaries and is linked to specific altitude levels, allowing controllers to maintain a structured environment for handling traffic.

The other terms, such as zone, district, and region, while they may describe areas in various contexts of managing airspace or operational units, do not specifically refer to the defined responsibility areas that controllers manage within the ARTCC or TRACON framework. Thus, "sector" is the correct terminology widely recognized and used within the field of air traffic control for these specific operational responsibilities.