The marine painter was born in Tyne Street, Newcastle, the son of the baths-keeper in Westgate Road. He went to sea at an early age and then worked as a designer and draughtsman for a shipbuilder. Carmichael's studio overlooked New Road (now City Road) in Newcastle. After his marriage to Mary Sweet, this studio burned down: 'Well, we can begin all over again,' he is reported to have smiled.
Carmichael's early works are watercolours, but he began painting in oils in 1825. His set of illustrations Views of Newcastle and the Carlisle Railway date from 1839. Between 1838 and 1862, he was a frequent exhibitor at the Royal Academy, where his first picture was Shipping in the Bay of Naples. In 1845, Carmichael left Newcastle for London and he eventually died in Scarborough. William Bell Scott in his Autobiographical Notes (1892) recalls Carmichael saying after his first visit to London: 'I couldn't stand the dullness of a social evening - I couldn't stand it - so at last I started up and danced a hornpipe by myself; but I was soon stopped off, for instead of anybody else following my example, they looked at each other as if they thought I had gone mad!'
Carmichael has always been popular in the North East and there is a large painting entitled The Heroic Exploit of Admiral Collingwood at the Battle of Trafalgar in the hall of Trinity House in Newcastle, though the scene is actually the battle of Cape St Vincent (1797) where Collingwood commanded the Excellent. Carmichael's house at 4 Ravensworth Terrace, Gateshead has been preserved at Beamish Museum (as part of the terrace rebuilt there 1980-85) where it is now a recreated Victorian dental surgery. Carmichael wrote The Art of Marine Painting in Water Colours (1859) and The Art of Marine Painting in Oil Colours (1864).