A graduate of the University of Michigan and University of California, Berkeley, Spedding became an assistant professor and head of the department of physical chemistry at Iowa State College in 1937. His efforts at building up the school were so successful that he would spend the rest of his career there, becoming a professor of chemistry in 1941, a professor of physics in 1950, a professor of metallurgy in 1962, and ultimately professor emeritus in 1973. He co-founded, along with Dr. Harley Wilhelm, the Institute for Atomic Research and the Ames Laboratory of the Atomic Energy Commission, and directed the Ames Laboratory from its founding in 1947 until 1968.