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A number of models for the critical surface of Nb3 Sn, and in general A15 superconductors, have been developed in the past years. This paper compares the most common parameterizations using consistent notation. Although the parameterizations appear dissimilar at first sight, they are in reality all based on a fit of the normalized pinning force vs. the reduced field, and have similar scalings for the critical field and critical temperature based on a Unified Scaling Law. In this paper we take the various parameterizations as a basis for a generic scaling proposed for the characterization and production follow-up of the ITER Nb3 Sn strands. The accuracy of the scaling is estimated using the fitting residuals on various sets of Ic (B, T, ϵ) data available in literature. We discuss the results, and give our view of the work towards a unified, practical parameterization. [ABSTRACT FROM AUTHOR]