After graduating from Englewood High School, Carruthers entered the college of engineering at the University of Illinois at Urbana–Champaign, and received a Bachelor of Science degree in physics in 1961. Carruthers continued his graduate work at the University of Illinois Urbana-Champaign and earned a master's degree in nuclear engineering in 1962. Carruthers received a Ph.D. in aeronautical and astronautical engineering in 1964. For his Ph.D. Carruthers researched atomic nitrogen recombination.