Richards came from an artistic background in Germantown, Pennsylvania: his father was a well-known painter and his mother a writer. He originally had ambitions in astronomy but his poor eyesight and the influence of his professor, Josiah P. Cooke, turned him to chemistry. After obtaining his doctorate from Harvard (1888) he continued his studies in Germany before returning to Harvard to take up a professorship in chemistry (1894).

In his doctoral work Richards made an accurate measurement of the ratio of the atomic weight of oxygen to that of hydrogen. His career continued to be devoted almost exclusively to the more accurate determination of atomic weights. He obtained the atomic weights of approximately 60 elements, improving considerably on those achieved by Jean Stas in the 1860s. His determination of the atomic weight of silver, for example, lowered this from Stas's 107.93 to 107.88. In 1913 his team showed that lead present in uranium had a lower atomic weight than normal specimens of lead, thus supporting the idea that it was formed by radioactive decay. In 1914 Richards was awarded the Nobel Prize for chemistry for his work on atomic weights.

In the latter half of his life he became interested in more theoretical problems. In 1902 he published an article which seemed to anticipate some of the ideas of the heat theorem of Nernst; he also worked on the compressibility of the elements.