A 1-carat cubic zirconia (CZ) is not the same size as a 1-carat diamond, because the densities of the two materials are not equal, so the size of the two cannot be equal. Cubic zirconia is denser than a diamond, and when both are at equal carats, the CZ will weigh more.
It is also important to note that in the case of comparing cubic zirconia to diamond, size refers to the weight, not the physical stature. Cubic Zirconia provides an equivalency chart on its official website to help understand the difference between the weights. A range of popular cuts are listed, as well as instructions on how to measure a ring at home.