There exist several inherent trade-offs while designing a fair model, such as those between the model’s predictive accuracy and fairness, or even among different notions of fairness. In practice, exploring these trade-offs requires significant human and computational resources. We propose a diagnostic to enable practitioners to explore these trade-offs without training a single model. Our work hinges on the observation that many widely-used fairness definitions can be expressed via the fairness-confusion tensor, an object obtained by splitting the traditional confusion matrix according to protected data attributes. Our diagnostic optimizes accuracy and fairness objectives directly over the elements in this tensor in a data-dependent, yet model-agnostic fashion. We further leverage our tensor-based perspective to generalize existing theoretical impossibility results to a wider range of fairness definitions. Finally, we demonstrate the usefulness of the proposed diagnostic on synthetic and real datasets.