Critical reception H received favorable reviews from most music critics. Adam Greenberg from
Allmusic reviewed the parent album
Rainbow and favoured "Independent" and "Hanabi," but failed to mention "July 1st." He felt that "Hanabi" "focuses strongly on her vocal qualities as well as some interesting phrasing [...]," while he concluded that the song "Close to You" "[...] never quite gets off the ground, especially when compared to the ending track, ["Independent,"]" Greenberg, who had written the extended biography of Hamasaki on the same website, had listed "Hanabi" as one of her career standouts.
CDJournal had reviewed each track on their mini-review. For "Independent," the reviewer called it an "upper dance tune" and felt the song sounded "aggressive." Tetsuo Hiraga from
Hot Express commended the tracks. Regarding "July 1st" and "Independent," Hiraga praised the songs for showing positive messages and having more personality drawn towards the songs and said the songs had shown more "respect." Hamasaki hosted an online voting poll for fans to choose their favorite tracks to be featured on her
Ayumi Hamasaki 15th Anniversary Tour Best Live Tour. As a result, all three songs from
H were featured on the list.
H won the Song of the Year Award at the Japan Gold Disc Awards in 2003, alongside "Free & Easy" and "Voyage."
Commercial response (pictured), who claimed the annual number one with "
Can You Keep a Secret?" the previous year, came second behind Hamasaki's
H.
H debuted at number one on the
Oricon Singles Chart and peaked at number one for three nonconsecutive weeks, including its debut week, its second week and its fourth week on the chart, with the third week being occupied by
Misia's single "
Nemurenu Yoru wa Kimi no Sei." The single stayed in the top ten for seven weeks, slipping to number thirteen in its eighth week. "H" also debuted at number one on
Tokyo Broadcasting System's (TBS)
Count Down TV chart during the chart week of August 3, 2002, her thirteenth single to do so.
H sold over one million units in Japan and was certified Million by the
Recording Industry Association of Japan (RIAJ) in November 2002 for shipments of one million units. "Traveling" and
H were the only singles of the year to be certified for one million copies shipped by RIAJ.
H also remains Hamasaki's last single to sell over one million units and is the only million-selling single on
Rainbow. It is her fourth single to sell over one million physical units, after "Boys & Girls" and
A from
Loveppears (1999), "Seasons" from
Duty (2000) and "M" from
I Am.... Hamasaki's last highest-selling single close to the one million physical sales mark was the next single "Voyage" which peaked at number one, but only sold an estimated 679,000 units in Japan and was certified double platinum. The song "Hanabi" was a commercially successful
sleeper hit, becoming certified gold by the
Recording Industry Association of Japan in January 2015, for selling 100,000
legal downloads since its release twelve and a half years prior. ==Promotion==