Professor Fletcher took an honours degree in Mathematics and Physics at the New England University College (then a part of Sydney University), followed by a fellowship to Harvard University where he completed a PhD in theoretical solid-state physics in 1955.
He returned to Australia in 1956, working at the Radiophysics Division of CSIRO and afterwards at the University of New England, where he was a professor of physics (1963-83). Here his research interests included musical acoustics and studies on the physics of ice and water.
In 1983 Fletcher was appointed director of CSIRO's Institute of Physical Sciences, a position he held until 1987. He remained at CSIRO as a chief research scientist until 1995.
Since then he has been a full-time Visiting Fellow in the ANU Research School of Physical Sciences and Engineering, and is also currently an Adjunct Professor of the University of NSW.
He has published 7 books, over 200 research papers 6 patents, 5 reports and 4 booklets for schools.