The vorticity and divergence are two basic and important diagnostic physical quantities for the evolution process of the synoptic systems and phenomena in the common meteorological coordinate systems. In this paper, the formula between the vorticity in the isobaric coordinates (“p” coordinate) and one in the local rectangular coordinates (“z” coordinate) is obtained via coordinate transformation method. So done for the divergence. The results show that the expression forms of the vorticity and the divergence are exactly same in both coordinates, but they have essential differences. The vorticity in the “p” coordinate not only indicates the rotation of the air parcel around the vertical axis, but also implies the atmospheric baroclinity. Similarly, the divergence in the “p” coordinate not only expresses the relative variable ratio of the horizontal area of the air parcel, but also indicates the atmospheric baroclinity. In the area of the front, the difference of the vorticity is very obvious in “p” coordinate and “z” coordinate, and the same difference is found for the divergence. If the atmosphere is barotropic, the vorticity in the “p” coordinate equals that in the “z” coordinate. The same is true for the divergence. The vorticity and divergence both have the dynamic and thermodynamic natures of the atmosphere in the “p” coordinate.