The NWA biopic, produced by Dr Dre and Ice Cube, was expected to make around half that figure, having cost $29m (£18.5m) to make.
Exit polls showed audiences were evenly divided between genders, while 46% were African-American and 23% white.
Dr Dre’s soundtrack, Compton, is also top of the UK and US album charts.
The album is his first studio record in 16 years.
Ice Cube’s son, O’Shea Jackson Jr., plays his father in the movie which tells the story of the band’s rise to fame and takes its title from their debut album, released in 1988.
‘So much power’
“It really struck a chord with audiences. It’s a story that is resonating right now,” said Paul Dergarabedian, senior media analyst with box office tracker Rentrack.
“It was one of those records that was an important work and a very important expression of a particular viewpoint. To this day, that album has so much power.”
The other big new film release, The Man from U.N.C.L.E., took just $13.5m (£8.6m) over the weekend, entering the chart at number three.
“I was hoping for a little higher number, quite frankly,” said Jeff Goldstein, executive vice president of domestic distribution for Warner Bros.
The film was directed by Guy Ritchie and stars Henry Cavill and Armie Hammer as a pair of American and Russian agents during the Cold War-era.
Tom Cruise’s Mission: Impossible Rogue Nation took $17m (£10.8m), falling into second spot.
Fox’s Fantastic Four fell two places with $8m (£5.1m) to take the fourth place spot, while The Gift was fifth with $6.5m (£4.1m).
US and Canada box office top ten
1. Straight Outta Compton – $56.1m (£35.8m)
2. Mission: Impossible Rogue Nation – $17m (£10.8m)
3. The Man From U.N.C.L.E. – $13.5m (£8.6m)
4. Fantastic Four – $8m (£5.1m)
5. The Gift – $6.5m (£4.1m)
6. Ant-Man – $5.5m (£3.5m)
7. Vacation – $5.3m (£3.4m)
8. Minions – $5.2m (£3.3m)
9. Ricki and the Flash – $4.6m (£2.9m)
10. Trainwreck – $3.8m (£2.4m)
Watch the trailer below.