TOKYO — Relays require a different calculus than the rest of Katie Ledecky’s races. In the emotion of the moment, when your result impacts not only your own medal hopes but those of at least three teammates, it’s pointless to worry about stroke rates or overall race strategy. You might be forced to take off, as Ledecky did Thursday afternoon in the final of the 4x200-meter freestyle relay at the Tokyo Olympics, buried deep in third place. There’s only one strategy available at that point.

“I knew I was just going to let it go,” she said, “and go for it each lap of that race.”

Starting from Lane 5, swimming the anchor leg in a race in which Team USA was trailing Australia by a second and a half and China by nearly two, Ledecky unleashed the full fury of the most powerful female freestyle stroke in history — simultaneously pulling off her most impressive single swim of the Olympic meet and pushing Team USA to a silver medal that seemed nearly impossible when she dove into the water.

Ledecky split a world-class time of 1 minute 53.76 — by far the fastest leg of any of the 32 swimmers in the race and just 0.02 off the time she put up in the same leg of the same event at Rio de Janeiro 2016 — to chase down Australian counterpart Leah Neale (1:55.85) and push Team USA to the silver medal with a time of 7:40.73. She nearly caught China’s Li Bingjie (1:55.30) as well, but China (7:40.33) held on for a narrow win.

All three medal winners were under the previous world record time, put up by Australia at the 2019 world championships.

The race provided Ledecky with her third medal of the Tokyo Olympics — she previously took silver in the 400 free and gold in the 1,500 free — and ninth of her Olympic career, the fifth most of any American female Olympian. It also helped earn veteran Allison Schmitt (who split a 1:56.34 out of the leadoff leg) a 10th Olympic medal, fourth on the same career list, with only Natalie Coughlin, Jenny Thompson and Dara Torres (12 apiece) ahead of her.

“When Ledecky jumped in, we knew we were in that race and she was going to come home strong,” Schmitt said. “And she did just that.”

Ledecky’s monster 200 leg came just 24 hours after she had fallen short of the medal stand in the individual race at the same distance. Ledecky’s 1:55.21 in the women’s 200 free final Wednesday was good only for fifth place, a stunning result for the defending Olympic champion.

On Wednesday, however, Ledecky was facing a daunting 200-1,500 “double” with about 70 minutes between races, a reality that may have colored her approach to the former or at the very least preyed upon her mind as she prepared for it. After brushing off the disappointment, Ledecky returned to win gold in the 1,500.

“I wasn’t really disappointed” with the 200 outcome, she said. “It was a really tough schedule.”

Without the same set of complicating circumstances Thursday, Ledecky simply dove in and swam. Her coach, Greg Meehan, gave only one bit advice before the race, warning Ledecky not to go out too fast and burn herself out for the closing stretch.

“But I’ve had enough experience with that relay to know that even when I try to hold back that first 100, it’s still really fast, but I can still get home,” she said. “So I just kind of let it go and just raced.”

Ledecky was to be back at Tokyo Aquatics Centre on Thursday night for the preliminary heats of the 800 free, a race in which she is the defending Olympic champion, defending world champion and world record holder. The 800 free final, which will be Ledecky’s final swim of the Tokyo Olympics, will be Saturday.