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First-principles calculations allow for the prediction and interpretation of the intrinsic properties of a system. Density functional theory calculations of the electronic structure of the multi-band magnetic insulator Bi₂CrAl₃O₉ fail to corroborate experimental observations that suggest a magnetic ground state. Spin-polarized DFT calculations find basic agreement with antiferromagnetic order, which has been putatively observed at temperatures below T=79 ± 3K. We report here realignment of our results with experiment by inclusion of a Hubbard parameter U and Hund's exchange J found via linear response methods — suggesting that the properties of Bi₂CrAl₃O₉ are the product of inter-atomic and intra-atomic electron-electron correlations.