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Franklin Reuben Carpenter was born on November 5, 1848 in Parkersburg, West Virginia, United States; descended from a Sussex family which came to America with William Penn. His father, John Woodward Carpenter, died when Franklin was less than four years old. His mother, Sarah Rebecca (Taylor) Carpenter became a teacher at the Broaddus Seminary at Clarksburg and later was postmistress there.
Franklin's mother was financially unable to give her son the education he craved. At sixteen Carpenter was apprenticed to a jeweler and watchmaker but continued his studies under Dr. Late, the village physician, until he secured a teacher's certificate and was thus enabled to earn a better salary. He saved enough money to take a course in civil engineering at Rector's College in Pruntytown, West Virginia.
In 1878 Carpenter opened an engineering office in Georgetown, Colorado, where he had been principal of the schools. Some of his work for the next few years included the first survey of the "loop" above Georgetown, and the location of the Loveland Pass Tunnel. In 1886 he went to the Black Hills, attracted by the tin deposits. The following year he became dean of the Territorial (Dakota) School of Mines from which position he resigned two years later. From that time on, his life was devoted to mining engineering. At Deadwood he erected the Deadwood and Delaware Smelter and developed a new mode of operation in semipyritic smelting. In 1900 health conditions in his family necessitated his moving from the Black Hills. He went to Denver where he maintained a consulting mining engineering practise for the rest of his life. In 1904 he successfully turned his attention to the electrostatic concentration of the ores of the Nonesuch Copper Mine at Lake Superior. His last important work was the application of the Longmaid-Henderson process to the treatment of Sudbury copper ores, in which he showed that copper could be rendered soluble while the nickel remained insoluble, and a raw material for making nickel steel in the open-hearth furnace could be made by smelting the residual iron oxide for nickel-bearing pig iron. He contributed a score or more of valuable papers to the technical press, including "Ore-Deposits of the Black Hills of Dakota" and "Pyritic Smelting in the Black Hills". While in South Dakota he wrote a book on the geology of the Black Hills.
He was elected a Fellow of the Geological Society of America.
In December 1874 he was married to Annette Howe of Athens, Ohio. They were the parents of eleven children.
