Tubulin self-association is a critical process in microtubule dynamics. The early intermediate structures, energetics, and their regulation by fluxes of chemical energy, associated with guanosine triphosphate (GTP) hydrolysis, are poorly understood. We reconstituted an in vitro minimal model system, mimicking the key elements of the nontemplated tubulin assembly. To resolve the distribution of GTP- and guanosine diphosphate (GDP)-tubulin structures, at low temperatures (∼10 °C) and below the critical concentration for the microtubule assembly, we analyzed in-line size-exclusion chromatography-small-angle X-ray scattering (SEC-SAXS) chromatograms of GTP- and GDP-tubulin solutions. Both solutions rapidly attained steady state. The SEC-SAXS data were consistent with an isodesmic thermodynamic model of longitudinal tubulin self-association into 1D oligomers, terminated by the formation of tubulin single rings. The analysis showed that free dimers coexisted with tetramers and hexamers. Tubulin monomers and lateral association between dimers were not detected. The dimer-dimer longitudinal self-association standard Helmholtz free energies were -14.2 ± 0.4 kBT (-8.0 ± 0.2 kcal mol-1) and -13.1 ± 0.5 kBT (-7.4 ± 0.3 kcal mol-1) for GDP- and GTP-tubulin, respectively. We then determined the mass fractions of dimers, tetramers, and hexamers as a function of the total tubulin concentration. A small fraction of stable tubulin single rings, with a radius of 19.2 ± 0.2 nm, was detected in the GDP-tubulin solution. In the GTP-tubulin solution, this fraction was significantly lower. Cryo-TEM images and SEC-multiangle light-scattering analysis corroborated these findings. Our analyses provide an accurate structure-stability description of cold tubulin solutions.