We report density functional theory calculations of the structural, electronic, and thermodynamic properties of cerium orthovanadate ͑CeVO 4 ͒ employing the local density approximation ͑LDA͒, generalized gradient approximation ͑GGA-PBE͒, LDA+U, and GGA-PBE+ U functionals. The LDA+ U, GGA-PBE+ U, LDA, and GGA-PBE equilibrium volumes deviate by −2.4%, +3.6%, −7.4%, and −0.8%, respectively, from experimental results. DFT+ U ͑DFT͒ predicts an antiferromagnetic ͑ferromagnetic͒ insulating ͑metallic͒ ground state, which is in agreement with experimental observations. DFT+ U yields Ce and V ions in the III+ and V+ oxidation state, respectively. CeVO 4 can be obtained by the reaction between Ce 2 O 3 and V 2 O 5 ͓ 1 2 Ce 2 O 3 ͑s͒ + 1 2 V 2 O 5 ͑s͒ → CeVO 4 ͑s͔͒ under an inert atmosphere, which is described as exoenergetic ͉͑⌬H 0 ͉ = 1.6− 1.8 eV͒ by all functionals. The reaction 1 2 Ce 2 O 3 ͑s͒ + 1 2 V 2 O 5 ͑s͒ → CeO 2 ͑s͒ +VO 2 ͑s͒ is exoenergetic with ͉⌬H 0 ͉ = 0.75, 0.25, 1.70, and 1.24 eV for LDA+ U, GGA-PBE+ U, LDA, and GGA-PBE, respectively. Hence, V V+ is more easily reduced to V IV+ than Ce IV+ to Ce III+ , but the difference is small as obtained with DFT+ U, PBE+ U, in particular. The variation of this reaction energy is due to the different performance of the various approaches for the description of the change in oxidation state of cerium, IV+ to III+ ͓J. L. F. Da Silva et al., Phys. Rev. B 75, 045121 ͑2007͔͒. The small difference between the V V and Ce IV reducibilities may have consequences for the use of CeO 2 as support of V 2 O 5 catalysts in selective oxidation.