The inputs for the calculation of a numerical time scale are a set of radiometric dates with variable uncertainty in both time (in myr) and stratigraphic position (in biozones). For the Paleozoic and Mesozoic, these selected input dates are irregularly distributed with respect to a biostratigraphic scale derived from graphical correlation, constrained optimization, or successive biozonal units; and for the Cenozoic, the dates are correlated to relative seafloor distances of marine magnetic anomalies. Spline fitting combined with Ripley's Maximum Likelihood fitting of a Functional Relationship produces a linear time scale with error bars on the boundary ages and durations of geologic stages. These methods were applied to Ordovician—Silurian, Devonian, Carboniferous—Permian, the Permian—Triassic boundary, Late Cretaceous, and Paleogene date sets.