A membrane-bound or cytosolic enzyme that catalyzes the synthesis of cyclic adp-ribose (cADPR) from nicotinamide adenine dinucleotide (NAD). This enzyme generally catalyzes the hydrolysis of cADPR to ADP-RIBOSE, as well, and sometimes the synthesis of cyclic adp-ribose 2' phosphate (2'-P-cADPR) from nadp.