Haematopoietic stem cells drive blood production, but their population size and lifetime dynamics have not been quantified directly in humans. Here we identified 129,582 spontaneous, genome-wide somatic mutations in 140 single-cell-derived haematopoietic stem and progenitor colonies from a healthy 59-year-old man and applied population-genetics approaches to reconstruct clonal dynamics. Cell divisions from early embryogenesis were evident in the phylogenetic tree; all blood cells were derived from a common ancestor that preceded gastrulation. The size of the stem cell population grew steadily in early life, reaching a stable plateau by adolescence. We estimate the numbers of haematopoietic stem cells that are actively making white blood cells at any one time to be in the range of 50,000-200,000. We observed adult haematopoietic stem cell clones that generate multilineage outputs, including granulocytes and B lymphocytes. Harnessing naturally occurring mutations to report the clonal architecture of an organ enables the high-resolution reconstruction of somatic cell dynamics in humans.