The American Petroleum Institute (API) equation for internal leak of API connections is uniaxial because it ignores axial force and external backup pressure. The ISO 13679 (2002) standard 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. Triaxial hydrostatic behavior is modeled with the mean normal stress, and thread shear behavior is modeled 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 and correlation with finite element analysis (FEA) results are presented for an example case of a 7-in.35-ppf N80 long-thread-casing (LTC) connection. The new triaxial safety factor with two connection constants applies to all types of threaded connections, including tubing, casing, and drillpipe, so long as the two constants are evaluated with appropriate but simple physical tests.