A continuous countercurrent flow process for converting FGD gypsum to ammonium sulfate and calcium carbonate including countercurrent flows with internal recycle of liquids to maximize the purity of reaction products while minimizing reaction times, and further include embodiments of the process that provide a yield of both ammonium sulfate and calcium carbonate to be 97 to 100%, and embodiments that provide for processes having a total time of reaction being 8 to 12 minutes, the invention further including processes for removing contaminants from the FGD gypsum employing an acid rinse process and/or a slurry tank reactor process.