North America
Upon its release, "Problem" reached the top position on the iTunes singles chart in over 40 countries and the top ten in over 60 countries, including the United States, where it reached the summit in 37 minutes, hence breaking the previous record held by Taylor Swift, whose single, "We Are Never Ever Getting Back Together" (2012), reached the top spot on the iTunes singles chart with a record of 37 minutes, making "Problem" the fastest selling single in digital history. On April 29, 2014, Billboard reported that "Problem" would most likely sell more than 300,000 copies by the end of its first week of availability in the United States, as well as that the song could easily debut within the top 10 of the Billboard Hot 100 chart regardless of any added airplay or streaming points. In addition to its sales, which accounted for the majority of its debut chart points on the Hot 100, "Problem" began receiving early radio support. The song drew 293 first-day plays on 87 stations on the day of its release, according to Nielsen BDS. Pop Songs reporter KIIS Los Angeles led all stations with 17 first-day plays. Among all stations, "Problem" garnered 3.8 million in opening-day radio audience.
"Problem" officially debuted at number three on the Billboard Hot 100 chart on the week ending on May 7, 2014, becoming Grande's second single to debut in the top ten, and her second top ten overall at the time, the other being "The Way". It became the highest debuting song of 2014 at the time, and the highest debuting song since Eminem's "The Monster," featuring Rihanna. "Problem" boasted just 1.3% less points than John Legend's "All of Me", which claimed the Hot 100 top spot. In its second week, "Problem" fell one spot to number four despite gains in airplay and streaming, while Iggy Azalea's "Fancy" replaced it as number three. "Problem" returned to its number three peak the following week before moving to a new peak at number two in its fourth week on the chart; Azalea's "Fancy" moved to the top of both the Digital and Hot 100 charts, boasting 28% more overall chart points than "Problem". "Problem" remained in the runner-up spot the following week, holding that position for five consecutive weeks. The song stayed in the Hot 100's top 10 for the first 16 weeks of its chart run, making its number three debut on May 7, 2014, and dropping out of the top 10 on August 27, 2014.
On Billboard Pop Songs, the song debuted at number 28 and reached number 21 in its second week on the chart. It debuted at number 24 on Billboard Rhythmic Songs chart, it moved up eight places to number 16 in its second week on the chart and peaked at number one. It eventually reached number one on both the Billboard Pop Songs and Rhythmic Songs charts, becoming Grande's first number one single on both charts. "Problem" just missed the entry into the Billboard Radio Songs chart in its first week of availability. It officially entered in at number 30 on the chart, up 70% in audience impressions from 24 million to 41 million. It rocketed 14 spots to number 16 in its second week, granting it the Hot 100's top Airplay Gainer award. It reached the top 10 of the Radio Songs chart at number 10 in its third week on the chart, up 30% in audience impressions from 56 million to 73 million. The song reached a peak of Number 2 in its 7th week and remained there for 3 weeks. In addition to this, the track also debuted on the Streaming Songs chart at number nine in its first week and moved five spots to number four in its second week, with a weekly peak of 4.4 million and 6.5 million, respectively. It has since peaked at number two in its third week on the chart.
"Problem" debuted atop the Billboard Hot Digital Songs chart at number one, selling 438,000 copies in its opening week, thus earning Grande the highest first-week sales numbers of 2014 at the time and also her biggest digital song sales week ever, breaking her previous record held by "The Way", which sold 219,000 digital copies for the week ending April 5, 2013. It is Grande's first number-one single on that chart. It is the overall 9th biggest debut for a digital song and is the 5th largest by a female artist, behind Taylor Swift's "We Are Never Ever Getting Back Together" (2012), Katy Perry's "Roar" (2013), Swift's "Shake It Off" (2014) and Lady Gaga's "Born This Way" (2011). Further, at 20 years old, Grande became the youngest woman to debut with more than 400,000 downloads. "Problem" also became the highest debut for a collaboration of only female soloists since "Give Me All Your Luvin'" by Madonna, Nicki Minaj and M.I.A. debuted at number 13 on the chart following Madonna's Super Bowl XLVI Halftime Show performance in February 2012. "Problem" spent a second week at number one on the Digital Songs chart with an additional 235,000 units sold, despite a 46% drop. The song topped the chart again in its third week selling 248,000 units, before slipping one spot to number two in its fourth week on the chart, despite a 15% growth of 284,000 units. The song reached its first million sales mark in the United States on May 28, 2014. On May 29, 2014, it was certified platinum by the Recording Industry Association of America, becoming Grande's second song to be certified platinum. As of June 2020, "Problem" has sold 3.7 million copies in the United States.
In Canada, "Problem" debuted at number three on the Canadian Hot 100 on May 17, 2014, becoming her first top 10 single in that country. In its second week on the chart the song dropped 12 places to number 15. In its 3rd week the song rose back to the top 10 at number six. In its fourth week the song rose even higher to number 4. "Problem" was the first song to top the weekly Billboard Twitter Top Tracks chart on June 12, 2014.
