Using more geologically reasonable constraints on radiometric dates from tuffs in a cyclic mixed carbonate-siliciclastic succession in the Donets Basin, Ukraine, newer and more geologically accurate ages of stage boundaries are calculated for the Carboniferous period. These calculations assume astronomically forced (Milankovitch) cyclicity and use radiometric dates of ash layers in the stratigraphic record. Unlike previous work, measurement uncertainties are propagated through calculations to provide mathematically constrained uncertainty in the ages of the boundaries. This work uses more realistic errors in the known dates of zircons in the ash layers and does not assume an a priori value for the Milankovitch long-eccentricity period. These calculations are compatible with other previous methods of determining the boundaries and represent improvement over existing age constraints.