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One of the main goals of theoretical chemistry is to predict real-world properties of materials and reactions to aid experiments. However, accuracies of such predictions rely on the interplay of accuracies of underlying approximations: methods, basis sets, solvation models, etc. Moreover, in many cases dozens of computed values (e.g., total energies) are used to compute one observable quantity (e.g., product ratio). In this case it is not straightforward to propagate calculation uncertainty into the prediction, and–even more so–vice versa. In this work we develop a general approach for propagating computational uncertainties into predictions, as well as for “backpropagating” the observed error in a prediction into uncertainties of the computed values. We use this approach to analyze fidelity of various approximations often used in modeling chemical reactions.