Hall came from an impoverished family and was largely self-taught, though he did study briefly at Central College, McGrawville, N.Y., and at the University of Michigan. By 1858 he had acquired a minor position at the Harvard University observatory, where he did research and wrote papers. In 1863 he was appointed professor of mathematics at the U.S. Naval Observatory, in Washington, D.C., a position he held until his retirement in 1891. There he was chiefly concerned with planetary astronomy, the orbits of double stars, and determinations of stellar parallax. From 1896 to 1901 he was professor of astronomy at Harvard.