Dana was born at Fort Sullivan, in Eastport, Maine. He was a first cousin of James J. Dana and later would be the father-in-law of John C. Tidball. His father Nathaniel G. Dana, also a West Point graduate and officer serving in the 1st U.S. Artillery, was stationed at Fort Sullivan at the time, but his father died when Dana was eleven years old. Dana's paternal grandfather, Luther Dana, was a naval officer in the American Revolution, and his maternal grandfather, Woodbury Langdon, served as a member of the Continental Congress (with his brother John Langdon), and later a U.S. Senator and governor of New Hampshire.