Chinese characters are composed of radicals appearing in non-linear spatial configurations. Although the visual complexity of Chinese orthography has been widely recognized, the probability that a radical appears in a permissible position within a configuration is yet to be investigated. This understanding of what patterns of radicals are spatially arranged would be crucial for mastering Chinese orthographic knowledge. The present study aims to analyze the positions of 438 radicals extracted from 4,808 most frequently used Chinese characters according to 22 permissible positions. The results reveal three main findings. First, on average, each radical has 2.66 permissible positions. Second, 33% of the 438 radicals exhibit extremely high position-based regularity (i.e., they only appear in one particular position). Third, only the factor “non-character” could predict high position-based regularity. Overall, the findings spell out the statistical regularities underlying the composition of radicals and their arranged positions within different configurations. Supporting examples and the implications of these regularities for learning and teaching Chinese characters are offered and discussed.