A set of potassium sulfates presenting a variety of sulfur environments (K2SO4, KHSO4, K2S2O7, and K2S2O8) has been studied by S-33 solid state NMR at 21 T. Low natural abundance (0.75%) and small gyromagnetic ratio of S-33 presented a serious challenge even at such a high magnetic field. Nevertheless, using the QCPMG technique we were able to obtain good signals from the sites with C-Q values approaching 16 MHz. Assignment of the sites and the relative orientations of the EFG tensors were assisted by quantum mechanical calculations using the Gaussian 98 and CASTEP packages. The Gaussian 98 Calculations were performed using the density functional method and gauge independent atomic orbitals oil molecular clusters of about 100-120 atoms. The CASTEP calculations utilized periodic boundary conditions and a gauge-including projector augmented-wave pseudopotential approach. Although only semiquantitative agreement is observed between the experimental and calculated parameters, the calculations are a very useful aid in the interpretation of experimental data.