"Birthday" is a song by American singer Katy Perry from her fourth studio album, Prism (2013). She co-wrote the song with Bonnie McKee and its producers Dr. Luke, Max Martin, and Cirkut. The song was recorded in Studios across California, alongside MXM Studios, based in Stockholm, Sweden. Inspired by Mariah Carey's first album, critics compared "Birthday" to the work of other musicians like Prince and Daft Punk. Through double entendres in the lyrics of "Birthday", Perry makes sexual references while celebrating a partner's birthday. Capitol Records sent the track to mainstream and rhythmic radio on April 21, 2014 as the album's fourth single.

Following the release of Prism, the song entered the single charts of South Korea and France. After being released as an official single, it reached number one on the US Billboard Dance Club Songs chart and the Israeli TV Airplay chart, number three in South Africa, number seven in Canada, number 10 in South Korea, number 17 on the US Billboard Hot 100 chart, and the top 40 in nine additional countries. It would later be certified 3× Platinum by Australian Recording Industry Association (ARIA), 2× Platinum in Music Canada (MC), and Platinum in New Zealand and the United States.

A music video for the track was released on April 24, 2014. Primarily recorded with hidden cameras, it features Perry disguised as five different characters in birthday parties and other celebrations. The makeup effects for Perry were designed and created by Tony Gardner. Perry's portrayal of a Jewish character in the video sparked criticism. The song was also performed at Perry's Prismatic World Tour. Jess Glynne covered the song on BBC Radio 1's Live Lounge, as did Halsey on SiriusXM.

"Birthday" was written by Perry, Bonnie McKee, Cirkut, Dr. Luke, and Max Martin. The latter three produced the song and contributed to the instrumentation and programmed their respective instruments. The drums were played by Steven Wolf, while the horns were played by the Saturday Night Live Band, arranged by Lenny Pickett and engineered by Dave O'Donnell. Its audio engineering was done by Peter Carlsson, Clint Gibbs, Sam Holland, and Michael Illbert. The track was finally mixed by Serban Ghenea at the MixStar Studios in Virginia Beach, Virginia, accompanied by the mixing engineer, John Hanes. The song itself was recorded at various studios, including Luke's in the Boo in Malibu, California, Conway Recording Studios in Hollywood, California, Playback Recording Studio in Santa Barbara, California, MXM Studios in Stockholm, Sweden and Secret Garden Studios in Montecito, California.

The song leaked online on October 16, 2013, two days prior to the official release of Prism. On April 3, 2014, the singer announced on her Twitter account that "Birthday" would be released as the album's fourth single, posting its cover art as well. The art is based on a photograph, taken during a birthday party circa 1990, in which a blonde Perry and her sister Angela Hudson smile toward the camera; "puffy" letter balloons were "photoshopped" onto the cover to spell out Perry's name. The song title appears in candles over a floral cake. To promote the single, a lyric video for "Birthday" was uploaded onto Perry's Vevo account on April 10, 2014. It depicts a variety of cakes and sweets—among other confections—decorated with the song's lyrics and concludes with Perry lighting the last candle of a cake.

At the length of three minutes and thirty-five seconds (3:35), "Birthday" is primarily styled in the genre of disco. According to the sheet music published at Musicnotes.com by Kobalt Music Publishing America, Inc., "Birthday" has a tempo of 126 beats per minute. Written in the key of B major, it follows a progression of Emaj9–C♯m7–Emaj9–C♯m7–B. Perry's vocals range from B₃ to F♯₅. During a preview event for Prism, held in New York City, Perry described "Birthday" as her "attempt at writing" a song that American singer Mariah Carey would have included in her eponymous debut album. Since its release, its musical composition has been strongly compared to that of other works of Prince and duo Wendy and Lisa.

"Birthday" contains elements of funk-pop, synthpop, and disco house. The song is backed by a "busy but buoyant" instrumentation featuring a "deeply rhythmic impulse". Randall Roberts of the Los Angeles Times felt "Birthday" was a musically updated version of disco, achieved by replacing "cheesy strings" with "jerky breaks and synth washes". Its "joyful" lyrics present the commemoration of her partner's birthday as a metaphor for sexual intercourse. The bridge section of "Birthday", which sees Perry singing "Let me get you in your birthday suit / It's time to bring out the big balloons", was found by Ben Rattliff to resemble French duo Daft Punk's works.

AllMusic's Stephen Thomas Erlewine and Kitty Empire from The Guardian called "Birthday" one of the best tracks from Prism: Erlewine described it as a "glorious retro-disco explosion" and Empire found a "girly simpatico" in the song that sustains it. Marah Eakin from The A.V. Club felt the track was "pure fun". Jason Lipshutz of Billboard called it a "stone-cold stunner", going on to say the song "serves as pop music's (superior) answer to Swizz Beatz's "Everyday Birthday". He also felt it was the song with the "most smash potential" included in Prism. Chris Bosman of Consequence wrote that the song was a "irrepressible disco jam" and found it superior to Carly Rae Jepsen's album Kiss (2012).