Alexander Leicester McAulay was born to Alexander McAulay and Ida Mary Butler in November 1895, and registered in the Tasmanian district of Clarence. His father was a research professor of mathematics. Ida Butler was described in McAulay's obituary as a 'keen, free-thinking Tasmanian'.
Educated at The Hutchins School (Hobart) and the University of Tasmania, he obtained a B.Sc. (University of Tasmania, 1916), and a PhD (University of Manchester, c.1919), an M.A (Cambridge, c.1921).
After obtaining his B.Sc., he worked as a demonstrator in natural philosophy (University of Melbourne, July 1916-May 1917), before departing to England. While in England (January 1918 to May 1917), he undertook graduate research at the University of Manchester, obtained a B.A. by research from Cambridge, engaged in research for the Air Ministry, and worked as a research student under the direction of Sir Ernest Rutherford, whom he then followed to Cambridge, working in the Cavendish Laboratory for two years.
He was appointed lecturer in physics at the University of Tasmania in 1922, and professor of physics in 1926.
He was married to Marjorie Kathleen McAulay, a teacher at Glen Dhu State College, the Technical College, and Launceston State High School (B.A., University of Tasmanian), who drowned aged 27 in 1932.