Babbage, whose father was a banker, was born in Teignmouth and studied at Cambridge. He played a major role in ending the isolationist attitudes prevalent in British mathematical circles in the early 19th century. In 1815 he helped to found the Analytical Society, which aimed to make the work of Continental mathematicians better known in Britain. Babbage's interest in stimulating British scientific activity was by no means confined to mathematics. In 1820 he was a founder of the Royal Astronomical Society and in 1834 of the Statistical Society, and he continued to attack the British public for their lack of interest in science. Among his inventions were a speedometer, and the locomotive ‘cowcatcher’. Babbage also did mathematical work that contributed to the setting up of the British postal system in 1840. From 1828 to 1839 he was Lucasian Professor of Mathematics at Cambridge University.

Babbage is best known for his work in designing and attempting to build three mechanical computers. He had been struck by the discrepancies found in mathematical tables, and the persistence of error. “I wish to God these calculations had been executed by steam,” he lamented in 1821. Mechanical execution, he argued, would eliminate error. Consequently he began work in 1823 on the machine later known as his Difference Engine No. 1. It operated by the method of finite differences and thus allowed values of functions to be obtained by addition rather than by multiplication. The engine was an analog decimal machine in which numbers were represented by the rotation of various wheels. After a decade of work the project was abandoned when Babbage's credit ran out. It had cost £17,000, was 8 feet high, and was made from 25,000 parts.

He later designed a simpler version, Difference Engine No. 2, with only a third of the number of parts. Plans were drawn up in 1847 and offered to an uninterested government in 1852. Without financial support Babbage never saw the project develop beyond the design stage.

The more ambitious analytical engine, first described in 1834, was similarly unsuccessful. Unlike the Difference Engine, this was to be a general computing machine in the manner of a modern computer, and was intended to be programmed with punched cards. One of Babbage's more enthusiastic supporters in this work was Ada Byron, Countess of Lovelace.

In 1985, Doron Swade and his colleagues at the Science Museum in London set out to build a full-size Babbage computer based upon his original designs. They chose to work on No. 2 and hoped to have it ready for Babbage's bicentenary in 1992. The construction was carried out in full public view on the floor of the museum. It was completed in May 1991 and has worked satisfactorily ever since.

Babbage was influential in a number of other areas. His Reflections on the Decline of Science in England (1830) began the move to the professionalization of British science. In his On the Economy of Machinery and Manufactures (1832), a work closely studied by Marx, Babbage argued that industry could only flourish by adopting a scientific approach to both technical and commercial matters. He also campaigned against street noises and was largely responsible for ‘Babbage's Bill’ of 1864, restricting the rights of street musicians. The subject was sufficiently important to him to form a chapter in his revealing Passages from the Life of a Philosopher (1864).