Buchanan was born to Patrick C. and Margaret Graham Buchanan in Rich Valley, Smyth County, Virginia. He received an A.B. in 1856 and an M.A.
In the context of his early life, Buchanan was born to Patrick C. and Margaret Graham Buchanan in Rich Valley, Smyth County, Virginia. He went on to earn a foundational undergraduate degree from there in 1856 and later acquired further academic credentials.