The son of the 2nd Earl Stanhope, he was educated at Eton and the University of Geneva. While in Geneva, he devoted himself to the study of mathematics, and acquired from Switzerland an intense love of liberty.
In politics he was a democrat. As Lord Mahon he contested the city of Westminster without success in 1774, when only just of age; but from the general election of 1780 until his accession to the peerage on March 7, 1786 he represented through the influence of Lord Shelburne the Buckinghamshire borough of High Wycombe. During the sessions of 1783 and 1784 he supported William Pitt the Younger, whose sister, Lady Hester Pitt, he married on December 19 1774. When Pitt strayed from the Liberal principles of his early days, his brother-in-law severed their political connexion and opposed the arbitrary measures which the ministry favoured. Lord Stanhope's character was generous, and his conduct consistent; but his speeches were not influential.
He was the chairman of the "Revolution Society," founded in honour of the Glorious Revolutionof 1688; the members of the society in 1790 expressed their sympathy with the aims of the French Revolution. In 1794 Stanhope supported Muir, one of the Edinburgh politicians who were transported to Botany Bay; and in 1795 he introduced into the Lords a motion deprecating any interference with the internal affairs of France. In all these points he was hopelessly beaten, and in the last of them he was in a "minority of one"--a sobriquet which stuck to him throughout life--whereupon he seceded from parliamentary life for five years. He was elected a fellow of the Royal Society so early as November 1772, and devoted a large part of his income to experiments in science and philosophy. He invented a method of securing buildings from fire (which, however, proved impracticable), the printing press and the lens which bear his name and a monochord for tuning musical instruments, suggested improvements in canal locks, made experiments in steam navigation in 1795-1797 and contrived two calculating machines.
When he acquired extensive property in Devon, Stanhope projected a canal through that county from the Bristol to the English Channel and took the levels himself. Electricity was another of the subjects which he studied, and the volume of Principles of Electricity which he issued in 1779 contained the rudiments of his theory on the "return stroke" resulting from the contact with the earth of the electric current of lightning, which were afterwards amplified in a contribution to the Philosophical Transactions for 1787. His principal labours in literature consisted of a reply to Edmund Burke's Reflections on the French Revolution (1790) and an Essay on the rights of juries (1792), and he long meditated the compilation. of a digest of the statutes.
The lean and awkward figure of Lord Stanhope figured in a host of the caricatures of James Sayers and James Gillray, reflecting on his political opinions and his relationship with his children. His first wife died in 1780, and he married in 1781 Louisa, daughter and sole heiress of the Hon. Henry Grenville (governor of Barbados in 1746 and ambassador to the Porte in 1762), a younger brother of the 1st Earl Temple and George Grenville; who survived him and died in March 1829. By his first wife be had three daughters, one of whom was Lady Hester Stanhope. His youngest daughter, Lady Lucy Rachael Stanhope, eloped with Thomas Taylor of Sevenoaks, the family apothecary, and her father refused to be reconciled to her; but Pitt made Taylor controller-general of the customs, and his son was one of Lord Chatham's executors. His second wife was the mother of three sons. Lord Stanhope died at the family seat of Chevening, Kent, and was succeeded as 4th Earl by his son Philip Henry (1781-1855), who inherited many of his scientific tastes, but is best known, perhaps for his association with Kaspar Hauser.