For the design of tubular conical transitions, the axial, bending and hoop stresses at the junctions are required. Among the offshore design standards, API RP-2A, ISO 19902 and NORSOK N-004, various equations exist for the same stress quantity which may cause confusions. The quality of these existing stress formulae will be examined in this paper. The tubular conical stress equations used in the offshore industry started from Boardman's studies in the 1940s. Recently, Lotsberg re-formulated this problem and applied the results to SCF applications. This paper solves the same set of shell equations but formulated in a format different from these previous studies. This new format allows for an in-depth examination of existing code equations. In addition, the formulation as presented can be used for modifications to gain higher accuracy. Several recommended new stress formulae are provided. It is observed that the existing code provisions' accuracy quickly deteriorates for cases where plate thickness in tubular and cone are different. The recommended approach is based on theoretical framework of shell mechanics, and better facilitate tubular/cone force balances when compared to existing equations. The sectional relationships among moment, shear and hoop loads are also treated consistently using shell theory. The resulted improvements make the recommended formulae more accurate than the existing provisions.