Educated at Cambridge University, Coulson’s interests included mathematics, physics, chemistry and molecular biology. His use of quantum methods to study molecular structure led to election as a fellow of the Royal Society in 1950. He held academic posts at the University of St Andrews, University College, London, King's College, London, and Oxford University.
He wrote popular works on atomic and molecular structure. Raised as a Methodist, he became a committed Christian in 1930. Beside scientific works, he wrote Science, Technology and the Christian (1953) and Science and Christian Belief (1955), integrating his scientific and religious views. Coulson believed religious faith was essential for the responsible use of science. He championed the development of nuclear energy and encouraged scientists to help improve third world food production.