Carl Wilhelm Bøckmann Barth was born in Christiania (now Oslo), the son of Daniel Nikolaj Barth (1810-1880), a circuit judge. Barth served in the Royal Norwegian Navy from 1863 until 1884; retiring as a First Lieutenant.
Barth studied painting under Hans Gude at the Karlsruhe in Berlin from 1881 to 1883. He stayed from 1889-1890 partly in London; partly on study trips along the English coast, especially at Dover. He later traveled to Paris and Brittany 1896-1897. He was in Italy and Tunisia from 1902 to 1903. Additionally he made numerous study trips along the Norwegian coast as well as Skagen.
Barth served as Director of the Christiania Art Society from 1889 to 1895 and from 1898 to 1902. He served as Chairman from 1898 to 1901. He was a member of the National Gallery, Oslo and Chairman of the Artist Association 1891-1898. He is represented by three works in the National Gallery of Norway; Losbåt i høy sjø (1882), Strand ved Dover (1889) and Marine (1897).