Stephan Abel Sinding was born in Trondhjem as a son of mining engineer Matthias Wilhelm Sinding (1811–1860) and Cecilie Marie Mejdell (1817–1886). Sinding was the brother of the composer Christian Sinding and painter Otto Ludvig Sinding and the nephew of Nicolai Mejdell (1822–1899) and Thorvald Mejdell (1824–1908), and through the former a first cousin of Glør Thorvald Mejdell, who married Stephan's sister Thora Cathrine Sinding. Stephan Sinding was also a first cousin of Alfred Sinding-Larsen and the three siblings Ernst Anton Henrik Sinding, Elisabeth Sinding (1846–1930) and Gustav Adolf Sinding (1849–1925).