 Sinclair was born in Crossroads, Grange, Banffshire, Scotland, the son of James George Sinclair (March 9, 1879; Wick, Scotland – March 18, 1962; Vancouver) and Betsy Sinclair née Ross (December 12, 1878; Evanton, Scotland – September 18, 1959; Vancouver).He moved to Vancouver with his family in 1911 where his father, who had already immigrated a year earlier, was among the founders of Vancouver Technical Secondary School, the area's first vocational school, and served as the school's second principal from 1930 until 1944.Sinclair studied engineering at the University of British Columbia and was awarded a Rhodes scholarship in 1928 to study mathematics at St John's College, in the University of Oxford.