The API equation for internal leak of API connections is uniaxial since it ignores axial force and external backup pressure. ISO 13679 for qualification of premium connections is biaxial at best. It includes tension/compression but ignores backup pressure for both internal and external leak tests. For tubular design, this paper introduces a new fully triaxial safety factor for threaded connections with dependence on thread shear and hydrostatic pressure. Hydrostatic behavior is modelled with the Mean Normal Stress, and thread shear behavior is modelled with the shear component of the von Mises Stress. A Leak Line for use like the pipe body ellipse is proposed for quick leak assessment. Leak ratings are presented for an example case of 7-in. 35-ppf N80 LTC. The new triaxial safety factor with two connection constants applies to all types of threaded connections, including tubing, casing, and drill pipe, so long as the two constants are evaluated with appropriate but simple physical tests.