Context is a critical ingredient of ubiquitous computing. While it is possible to use specialized sensors and becons to measure certain aspects of a user's context, we are interested in what we can infer from using the existing 802.11 wireless network infrastructure that already exists in many places. the context parameters we infer are the location of a client (with a median error of 1.5 meters) and an indicator of whether or not the client is in motion (with a classification accuracy of 87%). Our system, called LOCADIO, uses Wi-Fi signal strengths from existing access points measured on the client to infer both pieces of context. For motion, we measure the variance of the signal strength of the strongest access point as input to a simple two-state hidden Markov model (HMM) for smoothing transitions between the inferred states of "still" and "moving." For location, we exploit the fact that Wi-Fi signal strengths vary with location, and we use another HMM on a graph of location nodes whose transition probabilities are a function of the building's floor plan, expected pedestrian speeds, and our still/moving inference. Our probabilistic approach to inferring context gives a convenient way of balancing noisy measured data such as signal strengths against our a priori assumptions about a user's behavior.