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The deployment of wireless LANs (WLANs) has been steadily increasing over the years and estimating the actual bit rate of a WLAN device is important for management and applications such as those that can adapt their transmission rates according to the network characteristics. We propose a simple and accurate active measurement technique to infer the bit rate of an IEEE802.11 device. The proposed method is based both on a recently proposed technique to infer the type of access network and on the packet pair approach, but adapted to take into account the overhead caused by the IEEE802.11 control and the existence of concurrent WLAN traffic. Furthermore, the technique does not require the WLAN to be the bottleneck link in the path from the measuring point to the end computer. Results from simulation and from measurements show that the approach is accurate to infer WLAN access point rates both in scenarios where the WLAN devices can adapt their rates as well as WLANs with fixed transmission rates.