Peter Carmichael was born in Fife on 21 March 1809, and was the son of James Carmichael, a local flax mill manager who later established a mill in Dundee. He was educated at Dundee Grammar School and apprenticed at Monifieth Foundry in the making of textile machinery. Carmichael worked as an engineer in London and Leeds until 1833 when he returned to Dundee to become mill manager for Baxter Brothers.
Peter Carmichael was made a partner in 1852 and senior partner in 1872 (on the death of Sir David Baxter), remaining in close association with the firm until his death on 6 May 1891. He was described as the 'great motive power in the development of textile manufacturing in Dundee'.
Peter married Margaret Carmichael (no relation), daughter of the engineer James Carmichael and they had three sons, James Drummond Carmichael, Charles Carmichael (who died in infancy) and William Baxter Carmichael, and a daughter Grace Margaret Carmichael. All of his children suffered periods of ill health and all predeceased their father.
In 1869 Carmichael purchased the estate of Arthurstone near Meigle in Perthshire, and in the 1880s erected a church at the nearby village of Ardler in memory of his son, James Drummond Carmichael (1849-1881). He has been described as an expert manager of men and inventor of machines and a concerned and active public citizen, with wide interests in nature, religion and church affairs, literature and art. Peter Carmichael was a noted philanthropist, giving generous donations to various churches, Dundee Royal Infirmary and the Mars Training Ship among many other causes. He was one of the founders of Dundee Sailors Home. When he died his estate was valued at £516,000 and his will included several bequests to charitable organisations including £3000 to Dundee Royal Infirmary.