Richard Price was born at Tyn-ton in the parish of Llangeinor near Bridgend in the county of Glamorgan on 23 February 1723. His father, Rice Price, was a Dissenting minister who had been an assistant to Samuel Jones, founder of the Academy at Brynllywarch. By all the accounts that have survived, Rice Price was a strict Calvinist who maintained an austere discipline in the home. Richard, however, rebelled against his father's theology at an early age, and though he upheld the puritan values inculcated by his parents, his religious beliefs became much more liberal and much more rationalist.

Price's father died on 28 June 1739 and his mother, Catherine, scarcely a year later. Richard then went up to London, where his uncle, Samuel Price, was an assistant minister to the famous hymnwriter Isaac Watts, at St Mary Axe in Bury Street. Once established in London, Price was entered at Coward's Academy in Tenter Alley, Moorfields, where he came under the instruction and the influence of John Eames, who had been a friend and a disciple of Isaac Newton. It was at this Academy that he was prepared for the ministry, which was to remain his vocation and his first concern throughout an extremely active career. It was at this Academy too that he received the training in mathematics that enabled him to make important contributions to the theory of probability, to actuarial science and to the growth and development of insurance.