We investigate the physical layer (PHY) security of a system with a base-station (BS), a legitimate user, and an eavesdropper, whose exact location is unknown but within a ring-shaped area around the BS. To this end, we present novel closed-form expressions for the secrecy outage probability, which take into consideration both the impact of fading, as well as the eavesdropper’s location uncertainty. The derived expressions are validated through simulations, which reveal that the level of uncertainty should be seriously taken into account in the design and deployment of a wireless system with PHY security.