He was born in Portland, Oregon the son of attorney Lewis Cox and Elinor Junkin Cox. After Lewis Cox died, Elinor Cox married John Latane, who became a professor at Johns Hopkins University in 1913. In 1915 Richard enrolled at JHU to study physics, but his studies were cut short when he was drafted for WW I. He stayed in the US after being drafted and returned to JHU after the war, completing his BA in 1920. He earned his PhD in 1924; his thesis was "A Study of Pfund's Pressure Gauge".
He taught at NYU from 1924 to 1943, before returning to JHU to teach. He studied probability theory and the scattering of electrons from electric eels. Richard Cox's most important work was Cox's Theorem.
His wife Shelby Shackleford (1899 Halifax, Virginia - 1987), who he married in 1926, was an accomplished artist and illustrated Richard's books on electric eels.
His publications included: