By acquiring or evolving resistance to one antibiotic, bacteria can become cross-resistant to a second antibiotic, which further limits therapeutic choices. In the opposite scenario, initial resistance leads to collateral sensitivity to a second antibiotic, which can inform cycling or combinatorial treatments. Despite their clinical relevance, our knowledge of both interactions is limited. We used published chemical genetics data of the Escherichia coli single-gene deletion library in 40 antibiotics and devised a metric that discriminates between known cross-resistance and collateral-sensitivity antibiotic interactions. Thereby we inferred 404 cases of cross-resistance and 267 of collateral-sensitivity, expanding the number of known interactions by over threefold. We further validated 64/70 inferred interactions using experimental evolution. By identifying mutants driving these interactions in chemical genetics, we demonstrated that a drug pair can exhibit both interactions depending on the resistance mechanism. Finally, we applied collateral-sensitive drug pairs in combination to reduce antibiotic-resistance development in vitro.