He was born in Dublin, the fourth son of the Reverend Cecil Crampton, vicar of Headfort, County Galway, and Nicola Mary Marsh, daughter of the Rev.
Another useful family connection was Charles Kendal Bushe, Lord Chief Justice of Ireland, who married the Baronet's sister Anne.
He was educated at Trinity College Dublin, where he was an outstanding student, and gold medallist; later becoming a Fellow of the university (1807–16) and Regius Professor of Law in 1816.
O'Connell opposed Crampton's appointment to the Bench, calling him "utterly incompetent", lacking in integrity, and chosen only due to his friendships with senior judges.
A strict advocate of temperance, who maintained that two-thirds of crime in Ireland was drink related, he refused to serve alcohol to his guests, and according to a much-repeated story, poured the entire contents of the St. Valery wine cellar into the nearby River Dargle.