Carl O. Dunbar was born in 1891 in Hallowell, Cherokee County, Kansas, the son of David and Emma (Thomas) Dunbar. He had one younger sister, Maud Lucy. The Dunbar family owned a wheat farm.

Dunbar received his bachelors from the University of Kansas in 1913 and his doctorate from Yale University in 1917, focusing his studies on geology. After working briefly as a geology instructor at the University of Minnesota, Dunbar returned to Yale in 1920 and remained there for the rest of his career. He served as curator of Invertebrate Paleontology at the Yale Peabody Museum, and from 1942 until his retirement he was also director of the museum.

Dunbar's research interests and publications focused on invertebrate paleontology, especially on brachiopods and fusulinids, as well as stratigraphy. His field trips took him to Newfoundland, Kansas, Nebraska, and elsewhere. Dunbar also remained dedicated to teaching and educating, teaching continuously for 39 years and publishing books on historical geology for undergraduate courses. He was also interested in serving his profession, including as a member of the editorial board, vice-president, and fellow of the Geological Society of America; fellow, treasurer, associate editor, and president of the Paleontological Society; chairman of the Committee on Stratigraphy for the National Research Council from 1934-1953; and holding memberships in the Society of Economic Paleontologists and Mineralogists, American Association of Petroleum Geologists, American Assoication for the Advancement of Science, and the Connecticut Academy of Arts and Sciences.

Carl Dunbar married Lora Beamer in 1914. They had two children, Carl Owen Dunbar, Jr. and Lora Louise. Lora Beamer Dunbar died in 1978 and Carl Owen Dunbar died in 1979.