Amorphous uranium oxides are known to arise via industrial processes relevant to the nuclear fuel cycle yet evade rigorous structural characterization. A promising approach is to develop statistical relationships between uranium–oxygen coordination environments and thermodynamic stability from which general statements about the likelihood of observing particular U–O arrangements can be made. The number of known crystalline uranium oxides is insufficient to build statistical relationships. We have developed a database of theoretical compounds using genetic algorithms with the density functional theory as a foundation to analyze coordination geometries in the uranium–oxygen phase space. We draw fundamental insights into the nature of uranium–oxygen interactions by correlating total energy with the coordination environment. The most stable configuration of U cations with O anions is in an environment with coordination numbers 5–8 in a cubic configuration. Higher and lower coordination numbers are observed only in metastable phases. General trends are observable in the relationships between the coordination number, density, and uranium fraction in each structure. The new insight into uranium coordination enabled by these analyses is foundational for further studies into the characteristic properties of individual uranium oxide materials and for elucidation of potential oxidation pathways for uranium metal.