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all explanations are taken from the madoka magica wiki
madoka kaname
Madoka is seen to be a very kind girl who attempts to help anyone to the best of her ability but is also shown to be quite timid. In the past timeline, Homura Akemi and she seemed to have switched personalities, Madoka being the risk-taker and Homura being the shy one.
sayaka miki
Sayaka is shown to act slightly tomboyish and heroic. She cares a lot for her friends, made clear by her immediately making the contract to become a magical girl just so she could save Madoka.
Despite acting tomboyish, she does have a girly side, shown by her interest in romance and classical music. However, her vision of love is very unrealistic.
She rarely thinks twice before acting on something and comes into conflict with others easily. When combined with her kindness and courage, those two traits make her ignorant and careless.
homura akemi
Ever since her arrival at Mitakihara Middle School, Homura is immediately depicted as being very intelligent, athletic, distant, and cold. It is revealed in episode four that she is only like this because she has seen so much suffering during her tenure as a magical girl. Because of this, she does not want Madoka Kaname to become a magical girl and tries to do anything in order to stop her from making a wish with Kyubey, going as far as to attempt to injure and even kill the cat-like creature. Despite her cold attitude towards others, she still very much cares for Madoka as it is her sole objective to protect her due to the countless amount of blood, sweat, and tears she has shed over her jumps in time.
mami tomoe
Mami Tomoe appears to be a very kind and cheerful girl, as seen in "I'm Not Afraid of Anything Anymore". She also reveals to Madoka Kaname that she is lonely and she tells her how and why she became a magical girl. Mami is very nice to everyone but she seems to dislike Homura Akemi. In Rebellion, it's seen that she took a liking to Bebe.
kyoko sakura
Kyoko is fairly stubborn and has a fiery personality. She can be self-centered when she wants to be, though this is just a facade she made to herself and to others. In reality, Kyoko is kind and sympathetic when she sees those who are close to her in trouble. After losing her entire family due to the wish she had made for her father, she promised to never sacrifice herself for others as she believes that it would only end in tragedy. It is thought that she was afraid of getting herself hurt again, as well as the people she cared for the most. Kyoko appeared to be very rude at first, and would often get into fights, almost killing Sayaka during a battle due to her own rage. However she proved she was actually someone with good intentions. Kyoko is initially threatening and vicious towards Sayaka, however this is later because Kyoko has made the same mistake Sayaka had made and is unable to watch her suffer any longer. Kyoko is very good at masking and internalizing her feelings to come off as a strong magical girl.
kyubey
Despite appearing and sounding somewhat human, Kyubey is an Incubator and has no personal understanding of human emotion. Despite appearing as an individual, Kyubey and the rest of the Incubators do not in fact seem to have a distinct sense of self. On the occasions where a Kyubey is killed, another will step out and continue to converse as if nothing had occurred.
iroha tamaki
Iroha is shy but determined. She is also kind to others. Her personality is much like Madoka Kaname's, but Iroha has a stronger will.
momoko togame
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Momoko is a friendly and strong older-sister figure.
tsuruno yui
Tsuruno is energetic and friendly. She has ambitions for her family's Chinese restaurant named Banbanzai.
rena minami
Rena is a tsundere who is awkward when interacting with others. Inside, Rena is actually just shy and acts like this to not come off as weak. She is also a fan of pop idols.