A defining characteristic of social complexity in Homo sapiens is the diversity of our relationships. We build various types of connections with people in families, schools, workplaces, neighborhoods, and online communities. How do we make sense of such complex systems of human relationships? By using natural language processing, online surveys, laboratory cognitive tasks, and computational modelling on diverse modern cultures across the world (n = 20,425) and ancient cultures across 3,000 years of history, we discovered a universal representational space of relationship concepts, comprised of five principal dimensions (formality, activeness, valence, exchange, equality) and three core categories (hostile, public and private relationships). Our work reveals the fundamental cognitive constructs and cultural principles of relationship knowledge and advances our understanding of human sociality.