Adams was born in Cambridge on 11 March 1952 to Christopher Douglas Adams (1927–1985), a management consultant and computer salesman, former probation officer and lecturer on probationary group therapy techniques, and nurse Janet (1927–2016), née Donovan.[4][5] The family moved a few months after his birth to the East End of London, where his sister, Susan, was born three years later.[6] His parents divorced in 1957; Douglas, Susan and their mother moved then to an RSPCA animal shelter in Brentwood, Essex, run by his maternal grandparents.[7] Each remarried, giving Adams four half-siblings. A great-grandfather was the playwright Benjamin Franklin Wedekind.[8]

Adams attended Primrose Hill Primary School in Brentwood. At the age of nine, he passed the entrance exam for Brentwood School. He attended the prep school from 1959 to 1964, then the main school until December 1970. Adams was 6 feet (1.8 m) tall by age 12, and stopped growing at 6 feet 5 inches (1.96 m). His form master, Frank Halford, said that Adams's height had made him stand out and that he had been self-conscious about it.[9][10] His ability to write stories made him well known in the school.[11] He became the only student ever to be awarded a ten out of ten by Halford for creative writing – something he remembered for the rest of his life, particularly when facing writer's block.[6]

Some of his earliest writing was published at the school, such as a report on its photography club in The Brentwoodian in 1962, or spoof reviews in the school magazine Broadsheet, edited by Paul Neil Milne Johnstone, who later became a character in The Hitchhiker's Guide. He also designed the cover of one issue of the Broadsheet, and had a letter and short story published in The Eagle, the boys' comic, in 1965. A poem entitled "A Dissertation on the task of writing a poem on a candle and an account of some of the difficulties thereto pertaining" written by Adams in January 1970 at the age of 17, was discovered in a cupboard at the school in early 2014.[12]

On the strength of an essay on religious poetry that discussed the Beatles and William Blake, he was awarded an Exhibition in English at St John's College, Cambridge (where his father had also been a student),[13] going up in 1971. He wanted to join the Footlights, an invitation-only student comedy club that has acted as a hothouse for comic talent. He was not elected immediately as he had hoped, and started to write and perform in revues with Will Adams (no relation) and Martin Smith; they formed a group called "Adams-Smith-Adams". He became a member of the Footlights by 1973.[14] Despite doing very little work – he recalled having completed three essays in three years – he graduated in 1974 with a 2:2 in English literature.[15]