Frozen is a very loose adaptation of The Snow Queen, first published in 1845 by fairy-tale impresario Hans Christian Andersen.
Late in the night, five-year old Princess Anna wakes her elder sister, eight-year old Princess Elsa to play using Elsa's snow magic. However when the magic goes awry, the royal family journeys to the legendary Valley of the Living Rock to seek the help of trolls who remove the magic from Anna, and her memory of her sister's ability. In order to protect Elsa from the world, she is ostracized from everyone, including Anna, leaving both sisters distraught and lonely. Their despair only escalates when their parents die after they go on a ship to sail somewhere when a storm erupts and a wave capsizes the boat.
Three years later, it is the day of Elsa's (Idina Menzel) coronation ceremony. Dignitaries from around the world are coming to visit, including the Duke of Weselton (Alan Tudyk), who wants to run Arendelle's profits dry. Nobody is more excited than Anna (Kristen Bell), as they are finally opening the gates to the kingdom. She is happy to see other people, and hopes for the possibility of meeting that special someone, but Elsa is still concerned about trying to control her powers. As she strolls out onto the streets, she bumps into a horse, which happens to belong to the charming and handsome Prince Hans (Santino Fontana) of The Southern Isles. Anna is instantly attracted to him. The coronation goes off without a hitch, despite Elsa's fears and she even takes time to connect with her sister at the party before Anna and Hans sneak off to spend the evening together, quickly realizing the mutual attraction between them. Hans proposes right on the spot, and Anna immediately accepts. Elsa refuses to grant her blessing on the marriage, setting off an argument between the sisters culminating in Elsa's abilities being exposed to the party guests.
Panicking, Elsa runs with Anna in hot pursuit. As she becomes more stressed and panicked, the weather starts turning colder: snow begins to fall and Elsa races across the fjord, freezing it with each step but turning the whole body of water into ice, trapping all the ships. She makes it to the North Mountain where she laments her failure at keeping the powers contained but quickly becomes more and more at ease and relaxed, free to use her powers as she pleases building a snow man, an ice palace, and an ice dress. The next morning Anna is on a hunt for Elsa, determined to return her to Arendelle, end the winter, and mend their relationship. She finds herself at Oaken's Trading Post where she meets Oaken (Chris Williams) and Kristoff (Jonathan Groff). Anna convinces Kristoff to take her to the North Mountain where the source of the winter is coming from. After an attack from wolves the pair meet the snowman Elsa created, named Olaf (Josh Gad) who shares his dreams of experiencing summer and agrees to lead them to Elsa's hideout.
The gang makes it to Elsa's palace. Anna and Elsa reunite, and while both are happy to see each other, Elsa still harbors fears of wounding Anna once again. Despite Anna's promising to stand by her sister and help her, Elsa only grows more agitated and nervous resulting in her magic flaring, this time striking Anna in the heart. Elsa, in desperation to get her sister to safety, creates a giant snow creature (that Olaf calls "Marshmallow") to throw them out. After they outrun the snow monster, Kristoff notices that Anna's hair is turning white, and he takes them to seek help. Kristoff leads Anna (who is slowly freezing) to the trolls. A mix-up occurs, and the trolls insist Anna and Kristoff get married. Before the two can be wed by Gothi The Troll Priest, Anna collapses and Grand Pabbieappears. According to him, only an act of true love can thaw a frozen heart or else Anna will freeze solid. Kristoff races back to Arendelle to get Anna to Hans, believing true love's kiss will save her.
Meanwhile, Hans, on a search for Anna after her horse returns to the kingdom without her, and the guards find the ice castle. While Hans battles Marshmallow the duke's men attack Elsa who fights back, nearly killing them both much to her own horror. At the end of the altercation Elsa's chandelier comes crashing down, knocking her unconscious. She wakes up shackled in a cell back in Arendelle. Hans pleads with her to undo the winter to no avail but Elsa replies that she can't due to the fact that she is unable to control her powers. Anna is returned to Hans, freezing more and more by the minute. She begs him to kiss her and break the curse but he refuses, revealing his plan all along was to marry into Arendelle's throne, because he is the youngest of twelve brothers and will never reach the throne. He leaves Anna to freeze to death and goes to kill Elsa. Also, he puts the fire out to prevent Anna from getting any heat and warmth.
Elsa escapes from prison when she learns Hans means to have her executed for treason and heads out into the blizzard on the fjord. In the castle, Olaf comes to Anna's rescue and reveals Kristoff is in love with her. The two then travel together out on the fjord to find him, where he is racing back to the kingdom. Hans cuts Elsa off and tells her Anna is dead because of her. In Elsa's despair, the storm immediately stops, giving Kristoff and Anna the chance to reach each other. But when Anna sees Hans is about to kill her sister, she chooses instead to save Elsa, throwing herself between Elsa and Hans; she freezes solid just as Hans' sword hits her instead of Elsa. After a few moments of despair, Elsa sees her sister has thawed and come back to life because she sacrificed herself to save her sister, constituting an act of true love.
Elsa realizes love is the key to controlling her powers and thaws the kingdom. Sometime later, Anna gifts Kristoff a new sled and reveals Elsa has named him the Official Ice Master for the kingdom and the two share a kiss. Hans is sent back to his own kingdom in chains where he will have to deal with his 12 older brothers for his deeds and Elsa cuts off trade with Weselton. Elsa promises to never shut the castle gates again and skates on the new ice rink with Anna.