Price graduated from Stuyvesant High School in 1960, and went on to earn a dual degree in physics and engineering from Cornell University in 1965. He earned his PhD in 1971 from Caltech under the supervision of Kip Thorne. He spent his career from 1971 to 2004 at the University of Utah, where he holds the title of emeritus professor. In 2004, he joined the Center for Gravitational Wave Astronomy at the University of Texas at Brownsville. As of 2015, he became senior lecturer in physics at MIT. He is also on the adjunct faculty at the University of Massachusetts Dartmouth.