Charles Babbage was born in Walworth, London, to Benjamin Babbage, a banker, and Betsy Plumleigh Teape. His early life was marked by periods of ill health, leading to intermittent schooling.

Babbage attended a boarding school in Alphington near Exeter, run by Reverend Stephen Freeman. The school, with its extensive library, sparked his early love for mathematics.

Due to his health and the family's move to East Teignmouth, Babbage received private tutoring. He then attended Holmdale Academy in Middlesex, run by Reverend Moore, where he excelled in mathematics, particularly algebra. His love of algebra was so strong, that when Moore decided to send Babbage back to his private tutor, Babbage found another private tutor to continue his studies, without Moore's knowledge.

Babbage returned to his family in Teignmouth and continued his studies with two private tutors. The first tutor was a clergyman near Cambridge. After that, he was tutored by a man in Oxford. These tutors weren't up to the level of knowledge that Babbage possessed, so he mostly self-studied.

Babbage entered Trinity College, Cambridge. However, he found the mathematical instruction there inferior to his self-study and independent exploration.

Babbage transferred to Peterhouse, Cambridge, likely due to its more mathematically focused curriculum or for personal reasons.

Together with John Herschel, George Peacock, and others, Babbage founded the Analytical Society, a group dedicated to promoting Leibnizian calculus and algebraic methods in place of Newtonian fluxions at Cambridge. This marked a significant shift in British mathematics.

Babbage graduated from Peterhouse, Cambridge, without honors, although he had performed admirably in mathematics during his studies.