Hopper was born Grace Brewster Murray in New York City.
She was the oldest in a family of three children. Her parents Walter Fletcher Murray and Mary Campbell Van Horne were of Dutch and Scottish descent, and attended West End Collegiate Church.
Grace was educated at two private schools for girls, namely Graham School and Schoonmakers School both in New York City.
Intending to enter Vassar College in 1923 she failed a Latin examination and was required to wait another year.
After graduating she undertook research in mathematics at Yale University.
Grace was curious as a child, a lifelong trait; at the age of seven she decided to determine how an alarm clock worked, and dismantled seven alarm clocks before her mother realized what she was doing (she was then limited to one clock).
For her preparatory school education, she attended the Hartridge School in Plainfield, New Jersey. Admiral Grace Murray Hopper received many awards and commendations for her accomplishments.
In 1969, she was awarded the first ever Computer Science Man-of-the-Year Award from the Data Processing Management Association.
In 1971, the Sperry Corporation initiated an annual award in her name to honor young computer professionals for their significant contributions to computer science.
In 1973, she became the first person from the United States and the first woman of any nationality to be made a Distinguished Fellow of the British Computer Society.
After four decades of pioneering work, Admiral Hopper felt her greatest contribution had been “all the young people I’ve trained.” She was an inspirational professor and a much sought-after speaker, in some years she addressed more than 200 audiences.
In her speeches Admiral Hopper often used analogies and examples that have become legendary.
Once she presented a piece of wire about a foot long, and explained that it represented a nanosecond, since it was the maximum distance electricity could travel in wire in one-billionth of a second.
She often contrasted this nanosecond with a microsecond – a coil of wire nearly a thousand feet long – as she encouraged programmers not to waste even a microsecond.
In 1930 Grace Murray married Vincent Foster Hopper, an English teacher from New York University.
A Vassar College Fellowship allowed her to study at Yale University and, also in 1930, Yale awarded her an MA.
In 1931 she began teaching mathematics at Vassar College as an instructor in the Department of Mathematics and she continued on the staff there until 1943, having been promoted by that time to an associate professorship.
Hopper was awarded her doctorate by Yale University in 1934 for a thesis New Types of Irreducibility Criteria which was supervised by Oystein Ore.
Hopper attended New York University as a Vassar Faculty Fellow in 1941.
When Hopper retired from the Navy in August 1986, at 80 years of age, she was the oldest active duty officer in the United States.
She had reached the rank of Rear Admiral, being promoted to the rank of Commodore in a White House ceremony in December 1983, then becoming Rear Admiral Hopper in 1985.
At a celebration held in Boston on the USS Constitution to celebrate her retirement, Hopper was awarded the Defense Distinguished Service Medal, the highest award possible by the Department of Defense.