Roy Armati was born in Mackay in Queensland, one of two sons of Percy Armati who was a pharmacist in the town. Both sons became doctors.
He graduated in medicine from the University of Sydney in 1936 with first-class honours. During 1937 and 1938, he held residency positions at Royal Prince Alfred Hospital. Pulmonary tuberculosis interrupted his training at RPAH, but he was able to return in 1941 to continue an association with the Hospital which was uninterrupted until his death in 1967. During the war years 1941-45 he had served as acting clinical assistant, student supervisor and tutor in clinical medicine. He remained as a clinical assistant in the thoracic unit after having provided loyal service in his teaching role for many years.
His interests had been initially in pathology and clinical haematology, but when he developed tuberculosis he diverted his attention to thoracic medicine. He set up practice in the MLC building with a particular emphasis on life insurance and industrial medicine. He developed special expertise in mathematical statistics and was considered to be particularly knowledgeable in meteorology.
He married Mary White and there were three children of this marriage - two sons and a daughter. He subsequently remarried but had no other family.