Book vs. Film
A film adaptation can never be exactly the same. Often for timing and pacing reasons not everything can be included – it can be disappointing for book fans to learn that a favourite moment or character has been cut.
That being said I feel that the film is a reasonably faithful adaptation of J.K. Rowling’s novel Harry Potter and the Philosopher’s Stone.
Below are some differences between the book and the film. This is by no means comprehensive.
Mr. Dursley’s very weird day
The first chapter of the novel is from the viewpoint of Vernon and Petunia Dursley, before their infant nephew Harry turns up on their doorstep. The film skips this and begins with Dumbledore, McGonagall, and Hagrid delivering baby Harry to the Dursley’s.
‘Young Sirius Black’
In the novel Hagrid tells Dumbledore the he borrowed the motorcycle from ‘young Sirius Black. Good foreshadowing on Rowling’s part for when Sirius appears later in the series. This line is omitted from the film.

Baby Harry
Mrs. Figg
The book also mentions Mrs. Figg who looks after Harry occasionally. This character has importance later in the series. She is also not mentioned on the film.
Harry’s blue eyes
In the book Harry has green eyes in the film he has blue eyes. The film did attempt to have Daniel Radcliffe wear coloured contacts but he was unable to because they irritated his eyes.

Harry has blue eyes in the film
Dudley and Petunia have dark hair
In the novel Mrs. Dursley is described as ‘thin and blonde’ in the film actress Fiona Shaw has very dark hair. Dudley is also described as being blonde in the book. He also has darker hair like his mother in the film.
Boa constrictor to Burmese python
In the film Harry talks to a Burmese python at the zoo in the novel it is Boa Constrictor. Also in the novel Dudley’s best friend Piers Polkiss accompanies the Dursleys and Harry to the zoo. The Piers character is not included in the film.

The Burmese python
Harry and Draco’s first meeting
In the novel Harry and Draco first meet in Madam Malkin’s robes shop. They meet again on the Hogwarts Express. In the film Draco and Harry meet at Hogwarts before entering the Grand Hall for the Sorting Hat Ceremony.
Hagrid takes Harry to Kings Cross Station
In the book the Dursleys drop Harry off at Kings Cross Station to catch the Hogwarts Express. In the film Hagrid takes Harry.

London to Hogwarts
Sorting Hat and School Song
In the novel the Sorting Hat sings a song. This and the school song are both cut from the film.
The Mirror of Erised
In the book Harry sees his entire extended family standing behind him when he looks at the Mirror of Erised. In the film only his parents are standing behind him.

Mirror of Erised
Detention in the Forbidden Forest
In the novel Harry and Hermione are given a detention after being caught by Filch after hours. Draco and Neville receive a detention from Proessor McGonagall when she catches them in the corridor. In the film Harry, Hermione and Ron receive a detention after Draco tells McGongall that he saw them in Hagrid’s hut after hours. Malfoy also receives a detention because he too was out of bed after hours.
Norbert and Charlie Weasley
In the novel Charlie Weasley and his friends take Norbert to Romania. In the film it is briefly mentioned that Norbert was taken away by Dumbledore.

Norbert, a Norwegian Ridgeback Dragon
Hufflepuff-Gryffindor Quidditch Match
The Hufflepuff-Gryffindor match that Snape referees is not included in the film. This means the part where Ron and Neville get into a fight with Draco, Crabbe and Goyle at the game is not in the film.
Professor Binns
Professor Binns is the History of Magic professor at Hogwarts School of Witchcraft and Wizardry. In the novel we learn that he died in his sleep in the staffroom and he has continued to teach as a ghost. This character was not included in the film.
Peeves
Another ghost not in the film is the troublesome mischievous Peeves. The late comedian and actor Rik Mayal was cast as Peeves but his scenes were cut from the film.
I would be interested of any other differences between the book and film that you may have noticed.