Carmichael, the son of a physician and a teacher, was born in 1898, in Germantown, Pennsylvania. He received his BS degree from Tufts University in 1921, and his PhD from Harvard University in 1924. He was a brother in the Theta Delta Chi fraternity during his time at Tufts. He became an instructor at Princeton University's Department of Psychology in 1924 and was appointed to assistant professor in 1926. For fourteen years, Carmichael taught at Brown University, focusing on an experimental psychology with primates. After being part of the Brown University faculty from 1927 to 1936, he left for the Univ. of Rochester. He was appointed president of Tufts University in 1938, serving until his departure for the Smithsonian in 1953.