Increasing evidence suggests that language complexity is sensitive to sociopolitical factors.While most quantitative research has focused on morphology and syntax, the complexity ofthe lexicons of the world languages can be expected to be sensitive to extralinguistic factorstoo. In this paper, we have implemented a mathematical method for calculating the complex-ity of kinship term systems. We have furthermore conducted principal component analysesaimed to determine whether this complexity is impacted by core features characterizing so-ciopolitical complexity, including the status of the language within its society, the size of thelanguage family that a language belongs to, the number of jurisdictional levels above thelocal community, the size of local communities, population size and density, fixity of resid-ence, and distance moved each year. For this, we have drawn upon independently constructeddatabases of sociopolitical and linguistic complexity (WALS, D-Place, Ethnologue, Glottolog,and KinBank). We found that social complexity positively correlates with the complexity ofkinship terms. We interpret this finding as suggesting that the languages spoken by complexsocieties develop greater expressive power in order to share decontextualized knowledge andknow-hows with strangers. We expect that our algorithm can capture the complexity of otherdomains of the lexicons of the world’s languages.