In Babbage's time, mathematical tables of all kinds were used in all sorts of practical activities. Insurance clerks and bankers as well as navigators, astronomers, and engineers used different types of tables to do their daily work. Babbage soon realized that not only did it take hundreds of mathematicians to compile these highly useful but very dull arithmetic tables, but that because of human error, they were not always perfectly accurate. Around 1820, he had an idea that he would pursue for the rest of his life. At an Analytical Society meeting, Babbage apparently looked at an error-filled table and stated that "all these mathematical tables might be calculated by machinery." Babbage soon set out to see if he could discover a cheaper and more accurate method of producing tables by what he called mechanical computation. In 1822, he built a small, hand-cranked model that could compile and print astronomical and logarithmic tables to an accuracy of six decimal places.

Babbage's machine so impressed the Royal Society that it gave its backing to his request of the British government for funding. How Babbage was able to succeed in this highly unusual request is not known, but as a person who had already almost single-handedly reformed British mathematics, he probably was listened to when he argued that the national government had an obligation to support science. He was given more than 17,000 British pounds to build a full-scale machine called a difference engine that would calculate navigational tables for the Royal Navy. He was supposed to do this in three years.

Progress was slow and very expensive, however, and Babbage was soon spending some of his own inheritance in order to keep going. One of the major practical problems he encountered was that his technical demands were so precise that very often new tools had to be designed and custom-crafted. By 1834, the difference engine was nowhere near completion and the government had withdrawn its support for the project, in part because of its ambitiousness and complexity.