Arbuscular mycorrhizal fungi form symbioses with ~70% of plant species, building hyphal networks that exchange nutrients for host-derived carbon. These tubular networks move ~1 billion metric tons of carbon per year into Earth’s soils. However, we have no quantitative understanding of the hyphal infrastructure required to carry out this resource transfer. We assembled data from 322 studies representing more than 16,000 soil cores across nine biomes and developed machine-learning models to predict hyphal densities globally. With robotic imaging of more than 300,000 hyphae, we calibrated a biomass model from our spatial predictions. We estimate that global topsoils contain 1.10 × 10¹⁷ ± 0.13 × 10¹⁷ SD kilometers of living hyphae, weighing ~300 ± 60 SD megatons, ~4-to 6-fold the biomass of humans.