He was born at Coln St Denis, Gloucestershire, in 1818. He was educated at Pembroke College, Oxford, of which college (after taking a first class in mathematics in 1840 and gaining the university mathematical scholarship in 1842) he became fellow in 1844 and tutor and mathematical lecturer in 1845. He at once took a leading position in the mathematical teaching of the university, and published treatises on the Differential calculus (in 1848) and the Infinitesimal calculus (4 vols., 1852–1860), which for long were the recognized textbooks there. This latter work included the differential and integral calculus, the calculus of variations, the theory of attractions, and analytical mechanics.
In 1853, he was appointed Sedleian professor of natural philosophy, resigning it in June 1898. His chief public activity at Oxford was in connection with the Hebdomadal Council, and with the Clarendon Press, of which he was for many years secretary. He was also a curator of the Bodleian Library, an honorary fellow of the Queen's College, a governor of Winchester College and a visitor of Greenwich Observatory. In 1891, he was elected Master of Pembroke College, which dignity carried with it a canonry of Gloucester Cathedral. He also seems to have donated an interesting astronomical clock to Gloucester cathedral. He died in December 1898 and was buried in Holywell Cemetery, Oxford.
Nowadays, Professor Price is best remembered as one of the teachers of Lewis Carroll. There is a reference to his nickname of 'the bat' in the Mad Hatter's song "Twinkle, Twinkle, Little Bat", a parody of "Twinkle Twinkle Little Star" in Alice's Adventures in Wonderland.
- An essay on the relation of the several parts of a mathematical science to the fundamental idea therein contained (1849)
- A Treatise on Infinitesimal Calculus v. 1: Differential calculus (1857)
- A Treatise on Infinitesimal Calculus v. 2. Integral calculus and calculus of variations
- A Treatise on Infinitesimal Calculus v. 3. Statics attractions, dynamics of material particle
- A Treatise on Infinitesimal Calculus v. 4: The dynamics of material systems (1862)