Géza Kádas began his swimming career in 1938 with his classmate Gyula Válent. From 1946 to 1954 Kádas competed for Egri Barátság SE. Between 1946 and 1953 he won a total of 13 individual Hungarian championship titles and was a member of the Hungarian national team from 1946 to 1954. At the World College Games in Paris in 1947, Budapest in 1949 and Berlin in 1951, he won four championship gold medals, and one in Budapest in 1954. At the 1947 European Championships in Monte Carlo, he won a bronze medal in the 4 x 200 metres freestyle relay and finished fourth in the 100 and 400 metres. At the 1948 London Olympics Kádas finished second in the relay, third in the 100 metres, and fourth in the 400 metres, setting a European record in the latter. In 1952 he was fifth in the relay and in the 100 metres at the Helsinki Olympics. In 1954 he became the European champion in the relay in Torino and finished third in the 100 metres.
During his sports career Kádas worked as an official. In 1948 after his Olympic success, he became an accountant. Later, he was the deputy director of the Eger Water and Sewerage Works. He was the President of the social swimming association operating alongside the Eger VTSB, and a member of the board of the national Fáklya (Torch) Sports Association. He exposed himself during the 1956 revolution and was sentenced to eight years in prison in 1957. He was released from the Vác prison in 1961 with an amnesty and worked as an auxiliary worker at his old company. In 1967 Kádas moved to Budapest where he lived off odd jobs.