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802.11-based indoor positioning systems have been under research for quite some time now. However, despite the large attention this topic has gained, most of the research focused on the calculation of position estimates. In this paper, we go a step further and investigate how the position error that is inherent to 802.11-based positioning systems can be estimated. Knowing the position error is crucial for many applications that rely on position information: End users could be informed about the estimated position error to avoid frustration in case the system gives faulty position information. Service providers could adapt their delivered services based on the estimated position error to achieve a higher service quality. Finally, system operators could use the information to inspect whether a location system provides satisfactory positioning accuracy throughout the covered area. For position error estimation, we present four novel algorithms that take different features into account. Advantages of the combination of these four algorithms are explored by using a machine-learning approach. We evaluate our proposed algorithms in two different real-world deployments by using real-world data and emulation. The results show that our algorithms work independently of the environment and the positioning algorithm, and with an average precision for estimating the position error of up to 1.45 meters. The algorithms can --- by adjusting parameters --- realize different tradeoffs between underestimating and overestimating errors. Furthermore we comment on the algorithms' space and time complexity.