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• Multiple terminations of surfaces (10 1 ¯ 0) , (10 1 ¯ 1) , (11 2 ¯ 0) , and (0001) of Y(OH) 3 are established. • Effects of temperature and partial pressure of water and oxygen are included through first-principles thermodynamics. • The equilibrium morphology is of elongated hexagonal bipyramid enclosed by stoichiometric surfaces. Yttrium hydroxide Y(OH) 3 is an important precursor for yttrium oxides, and its morphologies are inherited by the yttrium oxides, thus affecting the products' properties and performance. Hydrothermally synthesized Y(OH) 3 particles are typically elongated hexagonal bipyramid, but thermodynamic parameters are inadequate for quantitative modeling of the morphology. We calculate surface energies and surface stresses of low-index orientations using density functional theory, and present a thermodynamic morphology model based on these parameters. We find that the thermodynamically stable surface terminations are always stoichiometric, and the surface energies are in the order of γ (10 1 ¯ 0) < γ (10 1 ¯ 1) < γ (11 2 ¯ 0) < γ (0001). The equilibrium morphology is of hexagonal prism capped by hexagonal pyramid enclosed by (10 1 ¯ 1) and (10 1 ¯ 0) surfaces. Because these terminations are stoichiometric, varying temperature or pressure is ineffective for modifying Y(OH) 3 particles' morphology, whereas surfactants should be used for this purpose in hydrothermal synthesis. Image, graphical abstract [ABSTRACT FROM AUTHOR]