NEW YORK — In the view of 18-year-old Emma Raducanu, comparing yourself or your results to those of others is “the thief of happiness.”

So it was fitting that Raducanu had no idea she had achieved a historic first Wednesday when she became the first qualifier to reach the U.S. Open semifinals, toppling her eighth consecutive opponent, Olympic champion Belinda Bencic.

Nor did Raducanu realize that, with her 6-3, 6-4 victory in the season’s final major, she will become the British No. 1 on Monday, when the world rankings are updated.

Raducanu joined Canada’s Leylah Fernandez, who clinched her semifinal spot Tuesday, the day after her 19th birthday, which she celebrated by passing out cupcakes to fellow players.

As the pressure mounts with each round at the U.S. Open, both teens’ happiness is palpable. It also has become infectious: Their stunning runs to the semifinals — Raducanu without conceding a set, Fernandez by upsetting three seeded players in consecutive three-set battles — have breathed new life into a tournament that was sadly star-depleted at the outset.

“We’re all just super hungry to make a difference in the tennis world,” said Fernandez, alluding not only to Raducanu, whom she has known since she was 12, but the cohort of teens making a mark in the sport, including 18-year-old Carlos Alcaraz of Spain, who won back-to-back five-set matches to reach the U.S. Open quarterfinals. “We want to make an impact in tennis. This tournament just proves how well we’re adapting to everything.”

Along the way, they have won over U.S. Open fans, who have embraced them as their own, particularly after the last American, Shelby Rogers, was ousted in the round of 16 by none other than Raducanu.

NBA legend Magic Johnson is among Fernandez’s new fans, tweeting: “19-YEAR-OLD LEYLAH FERNANDEZ DOES IT AGAIN! She becomes the youngest player to defeat two WTA Top-5 players at the same major since 17-year-old Serena Williams at the 1999 #USOpen

In Britain, London Mayor Sadiq Khan was among the first to congratulate Raducanu after her upset of the 11th-seeded Bencic on Wednesday, tweeting: “Another phenomenal performance. Emma Raducanu’s talent continues to shine bright as she storms into the US Open semi-finals after another straight sets win.”

Raducanu and Fernandez are not the hardest hitters or biggest servers in women’s tennis, but they are riding a mighty wave of self-belief, big-match poise and heady play that’s wildly entertaining.

The 5-foot-9 Raducanu is a coolheaded problem solver on the court with a reliable forehand and strong retrieval skills.

“The calmness and the mental strength definitely come from my upbringing,” said Raducanu, whose mother is Chinese and father is Romanian. “My parents have both instilled in me from a very young age to definitely have a positive attitude on court. ... When I was younger, it was definitely an absolute no-go if I had any sort of bad attitude.”

Though Fernandez is just 5-6, she toppled Grand Slam champions Naomi Osaka and Angelique Kerber in the third and fourth rounds with strokes and tactics that call to mind diminutive former world No. 1 Justine Henin, who absorbed opponents’ power and sent balls back with dizzying slices, spins and tempo.

But the tie that binds Raducanu and Fernandez, who are on opposite sides of the draw and would meet in Saturday’s final with one more victory each, is the absolute belief that they belong on the sport’s biggest stage.

It is as if the notion of not belonging on the court at 24,000-seat Arthur Ashe Stadium never occurred to them.

Fernandez, whose mother is Filipino Canadian and father is from Ecuador, said she has pictured this moment since she was a child.

“I’ve imagined myself playing on every tournament, every Grand Slam, at the biggest stage,” she said after her quarterfinal triumph over fifth-seeded Elina Svitolina. “I’ve always seen myself being in a big stadium in front of so many people and just having fun on the court.”

If Fernandez has shown a moment’s disbelief over what she has achieved at her second U.S. Open, it was upon winning the third-set tiebreaker that sealed the upset of Svitolina.

Fernandez dropped to her knees and buried her face in her hands as the crowd stood and cheered. When she stood, it was as if she realized she was the tournament’s rightful queen — on this day.

Raducanu, who was born in Toronto and moved with her family to London at age 2, has no less belief in her tennis. But she acknowledged after Wednesday’s upset of Bencic, her most formidable opponent thus far, that she was surprised to have achieved what she has now in her U.S. Open debut.

She turned pro in 2018 but continued her high school studies at a private school in London, juggling Britain’s competitive A-level exams with occasional tournaments in the ITF ranks, a rung below the elite WTA tour.

Granted a wild card at Wimbledon, she became a national sensation as she breezed through the early rounds. But in a wildly hyped fourth-round match, she developed breathing difficulties and was forced to withdraw.

Over the two months since, she has worked on her fitness and competed in lower-profile ITF events to improve her hard-court game and bolster her confidence in advance of the U.S. Open.

Because her current world ranking, 150th, isn’t high enough for a guaranteed spot in the U.S. Open’s 128-player main draw, Raducanu had to win three qualifying matches to get in.

She disclosed Wednesday that she had booked her return flight home to London for the day after qualifying, assuming that her attempt would end there.

“It’s a nice problem to have,” she said with a smile.

Among the TV viewers delighting in the palpable joy of the U.S. Open’s teen semifinalists is former tennis phenom Andrea Jaeger, who reached No. 2 in the world at 16 but was forced to retire at 19 with a major shoulder injury.

“Viva Teens in tennis!” Jaeger wrote in an email exchange Wednesday.

What enchants her about Fernandez and Raducanu, she explained, are a natural grace and exuberance that she feels makes their athleticism, talent and determination even more exciting. She predicts greatness for each, provided they keep joy at the center of their lives, on and off the court. And if she could share a word of advice, at 56, it is this: “Learn, grow and be aware beyond tennis, throughout life.”