A diverse immune repertoire is considered a hallmark of good health, but measuring diversity requires a framework that incorporates not only sequences’ relative frequencies but also their functional similarity to each other. Using experimentally measured dissociation constants from over 1,300 antibody-antigen and T-cell receptor (TCR)-peptide pairs, we developed a framework for functional immunological diversity based on binding and applied it to nearly 400 high-throughput antibody and TCR repertoires to reveal patterns in immunological memory, infection, vaccination, and aging. We show that functional diversity adds information that is not captured by raw diversity, revealing signatures of e.g. clonal selection, and that unlike raw diversity, functional diversity is a robust measure that does not require correction for sampling error. Finally, we show that according to functional diversity, unlike raw diversity, individuals’ repertoires overlap substantially, indicating a definable ceiling for the functional diversity of human adaptive immunity. Similarity redefines diversity in complex systems.