Microbial culture media, despite being potential troves of biological knowledge, are typically listed as natural-language media recipes and are not amenable to systematic study. To address this, we built a large relational Known Media Database (KOMODO) that includes >20,000 strain-media combinations and >3600 individual media variants along with compound concentrations (the entire collection of the Leibniz Institute -- DSMZ). KOMODO reveals a transitivity property that enables prediction of many new organism-media pairings, achieving 74% accuracy in new in vitro experiments. We next observe that phylogenetic and ecological similarity of organisms indicate their tendency to share lab media (ρ=0.57, p=4.5e-7, and ρ=0.87, p=4.5e-3 in Spearman correlations), which we use to build a collaborative filtering tool that can predict media for any organism (83% in new in vitro growth experiments). This work, including a website that predicts media given an organism’s 16S rDNA sequence, will markedly reduce the effort required to culture previously uncultivated microorganisms.