Born in New York, Floyd finished school at age 14. At the University of Chicago, he received a Bachelor's degree in liberal arts in 1953 (when still only 17) and a second Bachelor's degree in physics in 1958.
Becoming a computer operator in the early 1960s, he began publishing many noteworthy papers and was appointed an associate professor at Carnegie-Mellon University by the time he was 27 and became a full professor at Stanford University six years later. He obtained this position without a PhD.
Some of his contributions include a the design and analysis of efficient algorithm to find all shortest paths in a graph, and parsing, but perhaps his most significant achievement was pioneering the field of program verification using logical assertions with a paper in 1967, "Assigning Meanings to Programs".
Floyd worked closely with Donald Knuth, as the major reviewer for Knuth's seminal book The Art of Computer Programming, and is the person most cited in that work. The aphorism "Premature optimization is the root of all evil," often ascribed to Knuth, was actually coined by Floyd.
He received the Turing Award in 1978 "for having a clear influence on methodologies for the creation of efficient and reliable software, and for helping to found the following important subfields of computer science: the theory of parsing, the semantics of programming languages, automatic program verification, automatic program synthesis, and analysis of algorithms."
Floyd married and divorced twice, and had four children. His hobbies included backgammon and hiking.