A dimensionally adaptive, automatic switching algorithm is presented that has been developed for the RELAP5/PANBOX coupled thermal-hydraulics and neutron kinetics code system to switch between three-dimensional (3-D), one-dimensional (1-D), and point neutron kinetics models during a transient calculation. The switching criteria from higher- to lower-dimensional models are based on the time evolution of the flux shape, while the switching criteria from lower-dimensional models to the 3-D model are based on error estimates and reactivity criteria. Calculations of main-steam-line-break, control-rod-ejection, and boron-dilution transients have been used to validate the dimensionally adaptive automatic switching algorithm. These validation calculations show that the results produced by the automatic switching algorithm retain the accuracy of the 3-D reference calculations. Notably, they are considerably faster, typically requiring only 30 to 70% of the CPU time needed by the 3-D reference calculations. Furthermore, our calculations confirm that a 3-D neutron kinetics model is indeed required for these reactor safety transients by showing that the point-kinetics and 1-D models are by themselves very inaccurate.