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Family
Thomas Cochrane was born at Annsfield, near Hamilton, South Lanarkshire, Scotland, the son of Archibald Cochrane, 9th Earl of Dundonald and Anna Gilchrist. She was the daughter of Captain James Gilchrist and Ann Roberton, the daughter of Major John Roberton, 16th Laird of Earnock.

Cochrane had six brothers. Two served with distinction in the military: William Erskine Cochrane of the 15th Dragoon Guards, who served under Sir John Moore in the Peninsular War and reached the rank of major; and Archibald Cochrane, who became a captain in the Navy.

Cochrane was descended from lines of Scottish aristocracy and military service on both sides of his family. Through his uncle Admiral Sir Alexander Cochrane, the sixth son of the 8th Earl of Dundonald, Cochrane was cousin to his namesake Sir Thomas John Cochrane. Thomas Cochrane had a naval career and was appointed as Governor of Newfoundland and later Vice-Admiral of the United Kingdom. By 1793 the family fortune had been spent, and the family estate was sold to cover debts.

Early life
Cochrane spent much of his early life in Culross, Fife where his family had an estate.

Through the influence of his uncle Alexander Cochrane, he was listed as a member of the crew on the books of four Royal Navy ships starting when he was five years old. This common (though unlawful) practice called false muster was a means of acquiring the years of service required for promotion, if and when he joined the Navy. His father secured him a commission in the British Army at an early age, but Cochrane preferred the Navy. He joined it in 1793 upon the outbreak of the French Revolutionary Wars.