Black was born in Tyrie, Aberdeenshire, Scotland, the oldest and only son to John Black, from the parish on Tyrie, and Mary Leith, from the parish of Bodichell. Black also had two sisters, Ann and Mary. His baptism was witnessed by George Leith and Janet Black. It is noted in the baptism record that Black was "illegitimate," though, on June 24, 1781, John Black and Mary Leith are noted in the parish marriage records in Pitsligo as "having been contracted and claimed were married" prior to the birth of Samuel. Black's father died four years after Black's birth.