Clarke was born in Harrow in England. His father was Joseph Thacher Clarke, an archeologist. His older sister was the composer and violist Rebecca Clarke. Hans Clarke attended University College London School, and went on to enter the University as a student of chemistry, where he studied under William Ramsay, J. Norman Collie, and Samuel Smiles. He received a degree (Bachelor of Science) in 1908, and continued performing research at the University directed by Smiles and Stewart. In 1911 he was awarded an 1851 Exhibition Scholarship, which allowed him to study for three semesters in Berlin under Emil Fischer, and one semester with A. W. Stewart at Queen's College, Belfast. On his return he was granted the D.Sc. from London University in 1913.