An analysis is developed which permits fatigue lifetimes of components with pre-existing crack-like defects to be represented by a single expression which is a function of stress range and initial defect size; this is designated the Fatigue Intensity Factor (FIF). A graphical representation indicates that all such failures will fall upon a single, flat surface. The conventional S-N curve is shown to be a special case of this surface. Outliers from this surface may indicate deficiencies in estimates of stress range, of initial crack length, or that the failure is not due solely to fatigue. An equivalent analysis based upon the concept of threshold stress intensity indicates that a second, flat, intersecting surface exists. The conventional ‘fatigue limit’ often shown on S-N plots is shown to be a special case of this surface. Existing experimental data are used to define the surface, and examples of its application to the ordering of several potential fatigue failure locations within a single system and to interpreting non-standard fatigue failure are described.