William Bragg came on his father's side from a family without academic traditions, mainly yeoman farmers and merchant seamen. His mother was the daughter of the local vicar. Upon her death, when he was barely seven, he went to live with two paternal uncles who had set up a pharmacy and grocery shop in Market Harborough, Leicestershire. There he attended an old school reestablished by one of his uncles. He did well, and in 1875 his father sent him to school at King William College, Isle of Man. At first he found it difficult to adjust himself, but he was good at his lessons and at sports and finally became head boy. During his last year, however, the school was swept by a storm of religious emotionalism. The boys were frightened by the stories of hellfire and eternal damnation, and the experience left a strong mark on Bragg. Later he wrote, "It was a terrible year . . . for many years the Bible was a repelling book, which I shrank from reading." And in a lecture, Science and Faith, at Cambridge in 1941, he said, "I am sure that I am not the only one to whom when young the literal interpretation of Biblical texts caused years of acute misery and fear." On the other hand, he attributed his clear, balanced style of writing to his early grounding in the Authorized (King James) Version of the Bible; in The World of Sound he wrote, "From religion comes a man's purpose; from science his power to achieve it."

In 1882 he was granted a scholarship at Trinity College, Cambridge; and two years later he obtained third place in the Mathematical Tripos (final examinations), a splendid achievement that led to his appointment, in 1885, as professor of mathematics and physics at the young University of Adelaide, S.Aus. He then not only trained himself to become a good, lucid lecturer but also apprenticed himself to a firm of instrument makers and made all the equipment he needed for practical laboratory teaching. It was this early training that enabled him, later (in 1912), after his return to England, to design the Bragg ionization spectrometer, the prototype of all modern X-ray and neutron diffractometers, with which he made the first exact measurements of X-ray wavelengths and crystal data.

It was not until 1904, when Bragg became president of the physics section of the Australian Association for the Advancement of Science, that he began to think about original research. His subsequent work on alpha, beta, and gamma rays led the renowned British physicist Ernest Rutherford to propose him for fellowship of the Royal Society. He was elected in 1907 and within a year was offered a professorship in Leeds, England, where he developed his view that both gamma rays and X rays have particle-like properties.

In 1912 the German physicist Max von Laue announced that crystals could diffract X rays, thus implying that X rays must be waves like light but of much shorter wavelength. Bragg and his elder son, Lawrence, who was studying physics at Cambridge, then began to apply X rays to the study of crystal structure. These researches earned them jointly the award of the Nobel Prize for Physics in 1915.

After World War I, during which he worked on anti-submarine devices, Bragg established a school of crystallographic research at University College, London, and then, upon the death of the chemist and physicist Sir James Dewar, succeeded him as director of the Royal Institution and of the Davy Faraday Research Laboratories, London. To these institutions he attracted many young scientists whose researches he inspired and stimulated and who subsequently achieved fame. Bragg was also a popular scientific lecturer and writer. He gave "Christmas Lectures" for children, which, when published, became best-sellers. With Lady Bragg, he established a salon to which famous scientists came from far and wide. He was president of the Royal Society from 1935 to 1940 and received many other honours, but, to the last, he remained simple, gentle, and humble about his own success and proud of his son's.