Cram attended the Winwood High School in Long Island, N.Y. From 1938 to 1941, he attended Rollins College, in Winter Park, Florida on a national honorary scholarship, where he worked as an assistant in the chemistry department, and was active in theater, chapel choir, Lambda Chi Alpha, Phi Society, and Zeta Alpha Epsilon. It was at Rollins that he became known for building his own chemistry equipment. In 1941, he graduated from Rollins College with a B.S. in Chemistry.
Cram once admitted that his career wasn't without sacrifice. His first wife was Rollins classmate, Jean Turner, who also graduated in 1941, and went on to receive a master's degree in social work from Columbia University. His second wife, Jane, is a former chemistry professor at Mt. Holyoke College. Cram chose not to have any children, "because I would either be a bad father or a bad scientist."