Hopper, born Grace Murray, was educated at Vassar and at Yale, where she gained her PhD in 1934. She taught at Vassar until 1944, when she enlisted in the US Naval Reserve and was immediately assigned to Harvard to work with Howard Aiken on the Mark I computer, the ASCC (Automatic Sequence Controlled Calculator), for which she wrote the manual. Although she hoped to remain in the Navy after the war, her age prevented this and she had to be satisfied with the Naval reserve as a second choice. Consequently she remained at Harvard working on the Mark II and the Mark III computers.

In 1949 Hopper moved to Philadelphia to work with J. P. Eckhart and John Mauchly on the development of BINAC and remained with the company, despite several changes of ownership, until 1967. During this period she made a number of basic contributions to computer programming. In 1952 she devised the first compiler, a program that translated a high-level language into machine code, named A-O. She went on to produce a data-processing compiler known as Flow-matic.

It was apparent by this time to Hopper and other programmers that the business world lacked an agreed and adequate computer language. Hopper lobbied for a combined effort from the large computer companies and consequently a committee was established in 1959 under the guidance of the Defense Department to develop a common business language. Although she did not serve on the committee, the language developed by them, COBOL (Common Business Oriented Language), was derived in many respects from Flow-matic. For this reason Hopper has often been referred to as ‘the mother of COBOL’.

Although Hopper was forced through age to resign from the US Naval reserve in 1966 she was recalled a year later to work on their payroll program. She remained in the Naval reserve until 1986, having by then been promoted to the rank of rear admiral in 1985.