Nagel attended Los Angeles High School from 1941–1945 and played quarterback for the football team. He was a third team all-city selection his senior year in 1944. Nagel graduated in 1945 and enrolled at UCLA. He was a three time letter winner there from 1946–1949 as a quarterback and halfback for the Bruins. Nagel played for Coach Red Sanders and was named all-West Coast Conference and UCLA's Most Improved Player. He later earned bachelor's, master's, and law degrees from UCLA and was an assistant coach for the Bruins' football team.