I thought of Anna from Frozen!
Kristoff: "Calm down, calm down! Let the snowman be!"
Anna: "I'm calm, I'm calm!"
Kristoff: "Ok, good."
Anna: -throws snowball at snowman-
It is similar, but not the same thing. We use "relaxado" also for the muscles, like "Relaxa o corpo!". The word "calmo" is more like an opposite to anger/anxiety/stress. Another use of "relaxado" is like a sinonym of "irresponsible" (at least in South of Brasil). An example: "Ele é muito relaxado na escola".
"Calma" is also a noun: http://dictionary.reverso.net/portuguese-english/calma