After graduating from the University of Cape Town in 1944 Cormack pursued advanced studies there and at the University of Cambridge. He was a lecturer at Cape Town from 1950 to 1956 and then, after a year's research fellowship at Harvard University, became assistant professor of physics at Tufts University. His main research at Tufts centred on the interaction of subatomic particles. He advanced to full professor in 1964, was chairman of the department from 1968 to 1976, and retired in 1980. He became a U.S. citizen in 1966.

A part-time position as physicist for a hospital radiology department first aroused Cormack's interest in the problem of X-ray imaging of soft tissues or layers of tissue of differing densities. The two-dimensional representations of conventional X-ray plates were often unable to distinguish between such tissues. More information could be gained if X rays of the body were taken from several different directions, but conventional X-ray techniques made this procedure problematic. In the early 1960s Cormack showed how details of a flat section of soft tissues could be calculated from measurements of the attenuation of X rays passing through it from many different angles. He thus provided the mathematical technique for the CAT scan, in which an X-ray source and electronic detectors are rotated about the body and the resulting data is analyzed by a computer to produce a sharp map of the tissues within a cross section of the body. Cormack became a member of the American Academy of Arts and Sciences in 1980.