Katie Ledecky (far left) competes to break the world record in the women's 400-meter freestyle final at the Rio Olympics on Sunday. Photo: AFP

"Pure happiness" radiated from ­Katie Ledecky as the 19-year-old US freestyle phenom gazed at the scoreboard and contemplated her latest feat: 400-­meter freestyle Olympic gold in world record time.

Ledecky - targeting a rare 200-­meter, 400-meter and 800-­meter Olympic freestyle treble - surged home to touch the wall in 3 minutes 56.46 seconds, smashing her own world record of 3:58.37 set in the Gold Coast, Queensland in 2014.

Upon seeing her time, she grinned broadly, having achieved a goal she'd set herself back in 2013 of lowering the record in the event to "3:56 or ­better."

"To see 3:56 feels really good," said Ledecky, who now owns the six ­fastest times ever in the event and is one of the only two women ever to break 4 minutes.

Italy's Federica Pellegrini did it twice, in the era of the now-banned supersuits.

Ledecky, who has gone from strength to strength since her ­surprise win in the 800-meter ­freestyle as a 15-year-old in London, has broken 12 world records since then.

On Sunday, she covered the last 50 meters in a blazing 28.92 seconds, leaving Jazz Carlin of Great Britain to collect silver in 4:01.23 - 4.77 seconds adrift. American Leah Smith took bronze in 4:01.92.

"I just let it all out," said Ledecky, who came within a whisker of the world mark in the afternoon heats, clocking 3:58.71, the second-fastest ever until her gold medal swim.

Smith, who was thrilled to finish less than 2 seconds behind Ledecky in the 400-meter freestyle at the US trials, said she knew Ledecky was primed for something big.

Also on Sunday in Rio, US ­swimming great Michael Phelps helped the US men's team to victory in the 4x100-meter freestyle relay to collect his 19th gold medal at the Summer Olympics.