Born into the Carne banking family, he was educated at home and then at the Wesleyan School in Keynsham. As a child, Carne showed a fascination with geology and mineralogy and was in the habit of wondering around copper mines, buying mineralogical samples of ores and this formed the basis of his enormous mineralogical collection.  After his marriage to Mary Thomas (1808) he and his new wife lived in Rivière House, Phillack when he was manager of his family’s Cornish Copper Company's smelting works at Hayle but the family later moved to Chapel Street in Penzance.

Carne was particularly interested in the geology of St Michael’s Mount, and he reported his findings to the Royal Geological Society of Cornwall (February 11^th) together with his studies of the geology of, and mineral production in, West Penwith leading to his election to the Royal Society (May 28^th, 1818).  A committed Methodist, Carne made substantial donations to nearly all the Wesleyan Chapels in West Cornwall and this continued until his death on October 12^th, 1858.