Darwin was born in Cambridge, England into a scientific dynasty, the son of the mathematician George Howard Darwin and the grandson of Charles Darwin. His mother was Maud du Puy of Philadelphia, Pennsylvania. His elder sister was the artist Gwen Raverat, and his younger sister Margaret married Geoffrey Keynes, the brother of the economist John Maynard Keynes. His younger brother William Robert Darwin was a London stockbroker.

Darwin was educated at Marlborough College and, in 1910, he graduated from Trinity College, Cambridge in mathematics. He then secured a post-graduate position at the Victoria University of Manchester, working under Ernest Rutherford and Niels Bohr on Rutherford's atomic theory. In 1912, his interests developed into using his mathematical skills assisting Henry Moseley on X-ray diffraction. His two 1914 papers on diffraction of X-rays from perfect crystals became often cited classics.

On the outbreak of World War I, he joined the Royal Engineers, where he worked on problems in ballistics. From 1919 to 1922 he was a lecturer and fellow of Christ's College, Cambridge where he worked with R.H. Fowler on statistical mechanics and, what came to be known as, the Darwin-Fowler method. He then worked for a year at the California Institute of Technology before becoming Tait Professor of Natural Philosophy at the University of Edinburgh in 1924, working on quantum optics and magneto-optic effects. He also anticipated some of P.A.M. Dirac's relativistic theory of the electron.

In 1925 he married Katharine Pember, a mathematician. They had four sons and a daughter:

Cecily Darwin (born 1926) became an X-ray crystallographer and in 1951 married John Littleton of Philadelphia. George Pember Darwin (1928-2001) worked developing computers, and then 1964 married Angela Huxley, daughter of David Bruce Huxley. She was also a granddaughter of the writer Leonard Huxley and a great-granddaughter of Thomas Huxley, "Darwin's Bulldog". Henry Galton Darwin (1929-1992) was with the British Foreign Office, and married Jane Christie. Francis William Darwin (1932-2001) was a zoologist and taught at the University of London, and married in 1974. Edward Leonard Darwin (born 1934) became a civil engineer. In 1936 Darwin became master of Christ's College, beginning his career as an active and able administrator, becoming director of the National Physical Laboratory on the approach of war in 1938. He served in the role into the post-war period, unafraid to seek improved laboratory performance through re-organisation, but spending much of the war years working on the Manhattan Project coordinating the American, British, and Canadian efforts.

In his spare time, Darwin also served as a wartime vice-president of the Simplified Spelling Society.[1]

On his retirement, his attention turned to issues of population, genetics and eugenics. His conclusions were pessimistic and entailed a resigned belief in an inevitable Malthusian catastrophe, as described in his 1952 book The Next Million Years.

In later years he travelled widely, an enthusiastic collaborator across national borders and an able communicator of scientific ideas. He died in Cambridge.