King Agnarr

King Agdar and Queen Idun of Arendelle are minor characters in the 2013 Disney animated film Frozen. They are the parents of Elsa and Anna, and were the rulers of Arendelle until their deaths.

Names
Their names are not in the film's credits, but are seen written in the Runic alphabet on their memorial stone markers. According to those, the name of the king is Agðar (English: Agdar), and the name of the queen is Iðunn (English: Idun).
 * The Queen's Name: Iðunn can be anglicized as Ithunn, or Idunn/Idun. Iðunn means 'youthful', 'eternal youth' 'again to love'. Her English name could be Idun, because the name Idun is a popular name in Scandinavia, the setting of Frozen. The name Idun means 'rejuvenation'.
 * The King's Name: Agðar can be anglicized as Agdar. Agðar is a male form of Agða, a short form of Agatha, meaning 'good, honorable.' His English name could be Agdar; the name Agdar is a popular name in Norway. The name Agdar means 'brave warrior' in Norse and from greek agathos meaning 'good'.
 * Due to the Runic alphabet, the king's name can also be read as Akðar or Akthar. Some believe it could be the name Akhtar, which means 'star' and 'good luck'. The latter name is found in India, Pakistan and Bangladesh as well as Iran as a surname thus making it unlikely to be the given name of a Nordic King.

Background
King Agdar and Queen Idun were the rulers of Arendelle; greatly loved and respected by their subjects as well as their family. Together, they had two fair daughters, Elsa and Anna. Although Anna was a normal child, Elsa was born with powers of ice and snow. Apparently, Agdar and Idun were just as powerless as Anna, but it could be presumed that either magical abilities run in the family and merely skipped generations or that something happened to the queen when she was pregnant with Elsa.

Judging by how he presented himself, Agdar was learned, kind, powerful and diligent. Idun appeared to be far more passive than her husband, though given the obvious motherly nature needed to raise two daughters. With that, it was clear the rulers' primary priority were their daughters, willing to make large sacrifices to ensure their safety due to Elsa's unique abilities. And despite Elsa's powers, they didn't fear their daughter in the least, giving her just as much affection as Anna, and were even willing to make physical contact with her, but eventually decided against doing so, as Elsa preferred it that way, fearful she'd hurt them. And although they had faith in Elsa that she'll one day completely control her abilities, the fact that her life was as miserable as it was because of them devastated the king and queen, nearly driving Idun to tears at one point.

The Cursed Beginnings
The couple first appear after being frantically called by Elsa who accidentally struck Anna with ice magic while playing inside the castle. They are worried about Elsa's powers getting too strong, but fortunately they find a map in the royal library that will take them to some trolls who can help Anna.

Anna, Elsa, Agdar and Idun head over to the valley, and the king of the trolls, Pabbie, informs them Anna can be healed, though they're lucky she wasn't hit in the heart, for it can be fatal. Pabbie then informs the royal family that, while Elsa's magic is beautiful, she should learn to control it and not let fear consume her, or horrible things will occur. Agdar assures they'll help Elsa learn to conceal her powers until they can help her gain control of them, and before they depart, Pabbie wipes Anna's memories of Elsa's abilities, believing it's best if she completely forgot of the mystical moments they shared, though rearranging the memories to make it seem as if they were playing out in the regular snow, instead of snow conjured up in the castle.

The two sisters grow up separately to further safety upon Anna as well as keeping the castle gates closed for the kingdom's safety as well and vice-versa for Elsa. As Elsa grows, her parents try to help her control her magic ice powers. Agdar tells Elsa, "Conceal it, don't feel it, don't let it show" as a way to control her powers and to wear gloves to avoid conjuring the magic. It doesn't work completely, because Elsa can still freeze things without trying.

Tragedy Strikes
"You'll be fine, Elsa."

- The King's last words to Elsa

One day, the king and queen must set off on a two-week sea voyage (their intended destination is unknown). During a storm, they are drowned at sea by monstrous waves. Anna and all the people of Arendelle mourn their deaths (a portrait of the couple is draped over with a black sheet of fabric), but Elsa doesn't attend the funeral out of fear of her powers being revealed and someone getting hurt as a result, even though as the eldest sister, she is the heir to the throne. With their deaths, Elsa's training of her powers was left incomplete, as her powers were still mostly out of her control.

Agdar still appears later in the film; in a painting of his own coronation seen hanging in the library of the castle when Elsa was trying to control her powers, and again when the evil Prince Hans betrays Anna in order to take over the kingdom, though Idun makes no further appearances. They also are mentioned when Kristoff asks Anna during their arguement over Anna getting engaged to Hans, "Didn't you're parents ever warn you about strangers?" to which Anna replies "Yeah, they did."

Quotes

 * The King: "Elsa, what have you done? This is getting out of hand!"
 * The Queen: "Oh. She's ice cold!"
 * The King: "I know where we have to go."
 * The King: "Please! Help! It's my daughter!"
 * The King: "Uh, born. A-And they're getting stronger."
 * The King: "Do what you must."
 * The King: "It's for the best."
 * The King: "No! We'll protect her. She can learn to control it. I'm sure. Until then... We'll lock the gates. We'll reduce the staff. We will limit her contact with people, and keep her powers hidden from everyone. Including Anna."
 * The King: "The gloves will help. See? Conceal it. Don't let it show."
 * The King: "Getting upset only makes it worse. Calm down!"
 * The King: "You'll be fine, Elsa."

Trivia

 * Many fans have noted that Anna and Elsa's father bears a striking resemblance to Walt Disney in his younger years, and many think this was done to lovingly allude to him. He also sounds a lot like Walt too, especially when he tells Elsa that she will be all right when he and his queen depart on their sea voyage.
 * The possibility of this being intentional is quite high, as many fans also notice parallels between Elsa's and Anna's relationship to that of Mickey's and Oswald's ( characters who are often referred to as Walt's children ).
 * Both were separated from each other when they were fairly young. ( Elsa having to be put in another room to keep her away from Anna. The rights to Oswald's character being given to Universal Studios )
 * Both had little involvement with each others' lives despite being related.
 * Both were reunited by not the best of circumstances, which was unintentionally caused by the main character. ( Anna accidentally unveiling Elsa's powers, Mickey learning of Oswald in Epic Mickey after accidentally unleashing the Shadow Blot on the Cartoon Wasteland )
 * Since their reunion the two have become close, vowing to always be there for each other. ( Elsa returning to Arendelle with Anna, Oswald fighting along side Mickey in Epic Mickey 2 )
 * Both the King and Walt also died before the two could be reunited.
 * It should also be noted that like the King, Walt had two daughters, Diane Marie Disney and Sharon Mae Disney.
 * The king also somewhat resembles Haakon VII.
 * In the Frozen book illustrations, the king has dark hair and the queen has light hair, but in the movie, it's vice-versa.
 * The Queen's character model is a recoloured and customized version of Elsa's coronation model. There have been several differences, including her clothing and dark brown hair, and her face is thinner than both her her daughters, but her face and eyes mirror her oldest daughter's.
 * The accident with Anna strongly implies that Elsa's hair would have been brunette like her mother's if she never had her powers.
 * The King and Queen are the second set of Disney parents to die around about the same time in the movie, the first being Tarzan's parents. Tarzan and his parents were also involved in a shipwreck, though they survived it.
 * Also, both Frozen and Tarzan were directed by Chris Buck.
 * Some fans believe that the Queen of Arendelle may be related in some way to Rapunzel's mother, due to similarities in appearance between them, but there is no evidence whatsoever to support such speculation.
 * While it is widely speculated by fans that Rapunzel's mother and the Queen of Arendelle are closely related, they have only minor physical similarities, and it can be pointed out that the King of Corona looks closer to being related to Elsa and Anna's mother than the Queen of Corona has: (1) The King of Corona and the Queen Idun both have blue eyes, which Elsa and Anna share; the Queen of Corona has green eyes, which she shares with Rapunzel. (2) They both have the same hair texture and is rolled up, which Elsa and Anna also share; the Queen of Corona and Rapunzel share softer and straighter hair. (3) The Queen of Corona has a much darker skin tone than Queen Idun.
 * "Oh. She's ice cold!" was the Queen's only line in the film.
 * The ship the King and Queen were one that sank resulting in their deaths resembles the shipwreck Ariel and Flounder were exploring in their introductory scene in The Little Mermaid, just right before they are attacked by Glut the shark.