Smalley, the youngest of 4 siblings, was born in Akron, Ohio on June 6, 1943, to Frank Dudley Smalley, Jr., and Esther Virginia Rhoads.  He grew up in Kansas City, Missouri. Richard Smalley credits his father, mother and aunt as formative influences in industry, science and chemistry. His father, Frank Dudley Smalley, Jr. worked with mechanical and electrical equipment and eventually became CEO of a trade journal for farm implements called Implement and Tractor. His mother, Esther Rhoads Smalley, completed her B.A. Degree while Richard was a teenager. She was particularly inspired by mathematician Norman N. Royall Jr., who taught Foundations of Physical Science, and communicated her love of science to her son through long conversations and joint activities.  Smalley's maternal aunt, pioneering female chemist Sara Jane Rhoads, interested Smalley in the field of chemistry, letting him work in her organic chemistry laboratory, and suggesting that he attend Hope College, which had a strong chemistry program.
Smalley attended Hope College for two years before transferring to the University of Michigan where he received his Bachelor of Science in 1965, performing undergraduate research in the laboratory of Raoul Kopelman. Between his studies, he also worked in industry, where he developed his unique managerial style. He received his Ph.D. from Princeton University in 1973 after completing a doctoral dissertation, titled "The lower electronic states of 1,3,5 (sym)-triazine", under the supervision of Elliot R. Bernstein.  He did postdoctoral work at the University of Chicago from 1973 to 1976, with Donald Levy and Lennard Wharton where he was a pioneer in the development of supersonic beam laser spectroscopy.