Hippolyte was the younger brother of the founder of thermodynamicsSadi Carnot and second son of the revolutionary politician Lazare Nicolas Marguerite Carnot, who also served in the government of Napoleon. He was born at Saint-Omer, Pas-de-Calais. After the final defeat of Napoleon in 1815, his father went into exile. Hippolyte Carnot lived at first in exile with his father, returning to France only in 1823. Unable to enter active political life, he turned to literature and philosophy, publishing in 1828 a collection of Chants helléniens translated from the German of Wilhelm Müller, and in 1830 an Exposé de la doctrine Saint-Simonienne, and collaborating in the Saint-Simonian journal Le Producteur. He paid several visits to Britain and travelled in other countries of Europe.
In March 1839 after the dissolution of the chamber by Louis Philippe, he was elected deputy for Paris (re-elected in 1842 and in 1846), and sat in the group of the Radical Left, being one of the leaders of the party hostile to Louis Philippe. On February 24, 1848 he pronounced in favour of the republic. Alphonse de Lamartine chose him as minister of education in the provisional government, and Carnot set to work to organize the primary school systems, proposing a law for obligatory and free primary instruction, and another for the secondary education of girls. He opposed purely secular schools, holding that "the minister and the schoolmaster are the two columns on which rests the edifice of the republic." By this attitude he alienated both the Right and the Republicans of the Extreme Left, and was forced to resign on July 5, 1848. He was one of those who protested against the coup d'état of December 2, 1851, but was not proscribed by Louis Napoleon. He refused to sit in the Corps Législatif until 1864, in order not to have to take the oath to the emperor.
From 1864 to 1869 he was in the republican opposition, taking a very active part. He was defeated at the election of 1869. On February 8, 1871 he was named deputy for the Seine-et-Oisedépartement, and participated in the drawing up of the Constitutional Laws of 1875. On December 16, 1875; he was named by the National Assembly senator for life. He died three months after the election of his elder son, Marie François Sadi Carnot, to the presidency of the republic. 
He had published Le Ministère de l'Instruction Publique et des Cultes, depuis le 24 février jusqu'au 5 juillet 1848, Mémoires sur Carnot par son fils (2 vols., 1861-1864), Mémoires de Barère de Vieuzac (with David Angers, 4 vols 1842-1843). His second son, Marie Adolphe Carnot (b. 1830), became a distinguished mining engineer and director of the École des Mines (1899), his studies in analytical chemistry placing him in the front rank of French scientists. He was made a member of the Academy of Sciences in 1895.