The album's lead single, "Easier," was released on May 23, 2019, and 5 Seconds of Summer described it as "the first taste of their fourth album" in an interview with Rolling Stone.
In a May 2019 Ryan Seacrest interview, drummer Ashton Irwin commented on the musical direction of the then upcoming album, explaining, "[the band] had to agree to continue pursuing something [that was] fantastic and new [...] That's why the sound has changed".
The album's follow-up single, "Teeth," was released on August 21, 2019, and was featured in Season 3 of the Netflix series 13 Reasons Why.
On February 5, 2020, the band announced the album's release date, which was set for March 27, 2020, as well as the release of "No Shame," the album's third single.
The band revealed the album's title, Calm, was an acronym created from the first letters of each band member's name, Calum, Ashton, Luke and Michael. "[The fans] have been using that acronym for a long time," Hemmings explained, "and it kind of just sums up [that] we're a little bit older and a little bit wiser."
The band released "Wildflower" as the second promotional single on March 25, 2020, before releasing it to radio on April 17 as the album's fifth and final single. Due to the ongoing COVID-19 pandemic, song promotion was halted, and the song reached number twelve on the Australian Artists chart.
The COVID-19 pandemic and the stay-at-home order severely limited the album's promotion, forcing the band to cancel all promotional appearances and concerts. Instead of going "all over the world" for promotion, the band members did a number of radio and TV interviews via videocall and resorted to interacting with fans online via live streams and Twitter Q&As.
Hemmings performed an acoustic version of "Old Me" on The Tonight Show Starring Jimmy Fallon's "At Home Edition" on March 26, 2020.
Prior to the album's release, the band collaborated with Calm, a meditation app, to release a four-track Relaxation remix collection. The album includes four remixes, one by each member and one by producer Matt Pauling. Two singles are remixed on the compilation, with Michael Clifford remixing the album's lead single "Easier" and Calum Hood remixing the album's fourth single "Old Me." "Red Desert," remixed by Ashton Irwin, and "Best Years," remixed by Luke Hemmings, are among the non-singles included in the collection.