After graduating from Vassar College (B.A., 1928), Hopper attended Yale University (M.A., 1930; Ph.D., 1934). She taught mathematics at Vassar before joining the Naval Reserve in 1943. She became a lieutenant and was assigned to the Bureau of Ordnance's Computation Project at Harvard University (1944), where she worked on Mark I (Harvard Mark I), the first large-scale automatic calculator and a precursor of electronic computers. She remained at Harvard as a civilian research fellow while maintaining her naval career as a reservist. After a moth infiltrated the circuits of Mark I, she coined the term bug to refer to unexplained computer failures.

In 1949 Hopper joined the Eckert-Mauchly Computer Corp., where she designed an improved compiler, which translated a programmer's instructions into computer codes. She remained with the firm when it was taken over by Remington Rand (1951) and by Sperry Rand Corp. (1955). In 1957 her division developed Flow-Matic, the first English-language data-processing compiler. She retired from the navy with the rank of commander in 1966, but she was recalled to active duty the following year to help standardize the navy's computer languages. At the age of 79, she was the oldest officer on active U.S. naval duty when she retired again in 1986. She was elected a fellow of the Institute of Electrical and Electronic Engineers (1962), was named the first computer science Man of the Year by the Data Processing Management Association (1969), and was awarded the National Medal of Technology (1991).