The objective of this research was to determine the stress intensity multiplication factor (Y), as a function of the nondimensionalized crack depth (a/d), in the threads of a nut-loaded, aerospace, roll-threaded bolt under tensile fatigue conditions as a/d approaches zero. The proposed Y(a/d) solution can be used to improve fatigue crack growth life estimations. The research objectives were achieved through bolt material/stress state characterization, cyclic testing, and numeric modeling. The fracture analysis code FRANC3D was used because it could predict crack front shape and stress intensity factor (K). The numeric models predicted a changing crack front and stress intensity factors similar to the test data. The numeric studies accounted for the residual stresses measured by X-ray diffraction within the thread root of the test bolts. The FRANC3D model predicted Y(a/d) at shallow crack depths in the range of 0.01<a/d<0.11. By curve fitting the numeric and experimental data, a new Y(a/d) solution was determined: Y(a/d)=3079(a/d)⁶-6779(a/d)⁵+5757(a/d)⁴-2340(a/d)³+478.6(a/d)²-46.94(a/d)+2.506. The use of this Y(a/d) solution produces conservative crack growth life estimates relative to popular/benchmark methods. Based on test bolt fatigue data, greater accuracy may be possible with this Y(a/d) solution.