The social brain hypothesis has suggested that natural social network sizes may have a characteristic size in humans. This is determined in part by cognitive constraints and in part by the time costs of servicing relationships. Online social networking offers the potential to break through the glass ceiling imposed by at least the second of these, potentially enabling us to maintain much larger social networks. This is tested using two separate UK surveys, each randomly stratified by age, gender and regional population size. The data show that the size and range of online egocentric social networks, indexed as the number of Facebook friends, is similar to that of offline face-to-face networks. For one sample, respondents also specified the number of individuals in the inner layers of their network (formally identified as support clique and sympathy group), and these were also similar in size to those observed in offline networks. This suggests that, as originally proposed by the social brain hypothesis, there is a cognitive constraint on the size of social networks that even the communication advantages of online media are unable to overcome. In practical terms, it may reflect the fact that real (as opposed to casual) relationships require at least occasional face-to-face interaction to maintain them.