- A balloon pilot and a scientist find themselves in a fight for survival while attempting to make discoveries in a gas balloon in the 1860s.
- In 1862, pioneering meteorologist James Glaisher (Eddie Redmayne) teams up with daredevil balloon pilot Amelia Rennes (Felicity Jones) to advance human knowledge of the weather and fly higher than anyone in history. While their voyage to the very edge of existence helps the unlikely pair find their place in the world, they face physical and emotional challenges in the thin air, as the ascent becomes a fight for survival.
- In 1862 London, Amelia (Felicity Jones) and her sister, Antonia (Phoebe Fox), are traveling in a carriage to an unknown destination when Amelia has a panic attack and leaves the carriage. Antonia tries to talk her out of the upcoming balloon launch but Amelia refuses. Meanwhile, aspiring meteorologist James Glaisher (Eddie Redmayne) waits impatiently with his friend John (Himesh Patel, along with thousands of spectators, as it nears the time for his balloon launch. Eventually, Amelia, the balloon's pilot, arrives in a grand spectacle, putting on a show for the crowd much to the reserved Glaisher's chagrin. Despite being haunted by a vision of her late husband Pierre (Vincent Perez), Amelia keeps up the brave front and the balloon launches.
In a flashback, James appears before the Royal Society and explains his theory that the weather can be predicted. He is laughed out of the building, the jeers led by Charles Green. Returning home, he talks to his parents, who try to persuade him to pursue another avenue of science. On the balloon, James and Amelia start rising through the cloud layer (in 9 min and 23 secs, they are at 5450 feet). Both delight in the experience but soon run into a violent storm which sends the balloon spinning. In a flashback, Antonia persuades Amelia to attend a society function. There, Amelia is approached by James and dances with him to put off an approaching suitor. As they dance, James asks if she would be willing to be his pilot while he attempts to prove his theories. Amelia is angered when she realizes that James attended the dance to simply meet her but agrees to be his pilot. Days later, as she is assembling the balloon, Amelia is confronted by Antonia, who asks that Amelia give up on being an Aeronaut and try a more conventional career path.
After a close brush with death, with James suffering a head injury, they make it through the storm and continue rising. James releases the first of five pigeons carrying messages stating the current altitude along with other scientific readings in case they don't survive. As time passes, James and Amelia get to know each other and start to enjoy each other's company, with James becoming less concerned with his readings and starting to enjoy the experience. They discover an air current which is home to a flock of butterflies, confirming one of John's theories which James had always refuted. In a flashback, as James practices for the flight, Amelia approaches and tells him she's changed her mind. He is horrified, as money has already been spent, but she is unmoved and leaves. James goes to tell his father, suffering from dementia, but when his father speaks of his pride in James, it causes him to back out. Desperate, James approaches Green asking to accompany him on a flight. Green refuses, scoffing at the idea. John goes to see Amelia, showing her a book containing James' studies on snowflakes to show how much the flight would mean to James. Amelia goes to Pierre's grave to reflect. When it begins to snow, as James predicted, she decides to go with him after all.
Eventually, the balloon exceeds 23,000 feet, beating the record for the highest altitude and James releases another pigeon. Amelia finds out James didn't bring any clothes suitable for the rapidly decreasing temperature and decides to start descending. James refuses, and the two argue. Amelia agrees to keep rising, but makes it clear to James that they'll have to start descending soon. At 26500 feet, The temperature is now well below freezing and as James finds the last pigeon frozen, he throws it, some equipment, and sandbags overboard to speed up their ascent. James is experiencing Hypoxia from the altitude and insists they continue to climb. The two get into a scuffle, and James earns himself a slap from Amelia when he invokes Pierre's name (James suggests that Pierre risked Amelia's life in pursuit of fame, bu Amelia corrects him that she was the ambitious one and Pierre tried to stop her and when the mistake could not be rectified, he sacrificed himself so that she could live). She tells him the story of how Pierre sacrificed himself to save her during a balloon flight. This brings James to his senses, and he agrees to descend. Amelia discovers the gas release valve on top of the balloon is frozen. As James falls unconscious, she has no choice but to climb up the outside of the balloon and open the valve from the top. With frostbite setting in on her hands, she struggles upward and manages to open the air release slightly, wedging her boot in the valve, causing a slow release of the gas. Amelia loses consciousness and topples over the side but is saved by her rope tether. At its peak their balloon reached 36,010 feet.
When she awakens, Amelia manages to swing back to the balloon and wake James. As they continue to descend, snow begins to hovers around them, and they realize the balloon is collapsing from the loss of too much gas. They manage to close the gas release but it is not enough to slow their descent, so they throw everything they can over the side. When this doesn't work, they climb into the framework and release the basket. Amelia then prepares to sacrifice herself to save James, but James convinces her that they can use the balloon as a parachute, which slows their descent. They crash through trees and hit the ground hard, with Amelia being dragged along behind the balloon. She wakes and calls for James, who staggers towards her. Both are injured, but euphoric that they managed to survive. A voice-over by Amelia states that James' findings eventually paved the way for the first weather reports. James gives another speech to the Royal Society, and he and his field are finally accepted, earning a standing ovation from his fellows. James and Amelia go on another balloon flight together.
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