Nagel was the head coach at Utah (1958-65) and Iowa (1966-70), but his college career began at UCLA. He played for the Bruins from 1946-49. He threw for 969 yards in 1948 and shifted to tailback in 1949, Red Sanders' first season as coach. Nagel gained 84 yards rushing and threw for 230 yards that season. He also had a team-high three interceptions as a defensive back.
After finishing his playing career at UCLA, Nagel stayed on as the freshman team's coach. He was a varsity assistant in 1951 and 1952. He had a 58-71-3 record.
Nagel played for the Chicago Cardinals in 1953. He also served as athletic director at Washington State and Hawaii, as well as being the executive vice president of the Rams and executive director of the Hula Bowl.
He was inducted into the National Assn. of Collegiate Directors of Athletics hall of fame in 2006.