He was born in Appledore, near Bideford in Devon, and after a spell in the Navy, studied art at Plymouth and the Royal Academy Schools (1824). His early visionary work was greatly inspired by William Blake, and he became a member of the Blake-influenced group known as The Ancients which met at Samuel Palmer's in Shoreham, Kent in the later 1820s and early 1830s.
Amongst Calvert's finest works are exquisite miniature wood engravings which date from this early period; his wood and copper engravings all date from 1827-31, but were only seen by friends until published by his son in 1893 in an edition of 350. He also made etchings. In 1844 he visited Greece.
Much of his subsequent life was spent with his wife Mary, in Dalston and nearby Hackney, a short distance from London. His work from this later period (not considered his best) shows a Classical influence.