In 1862 London, Amelia, portrayed by Felicity Jones, and her sister Antonia, played by Phoebe Fox, embark on a mysterious journey in a carriage. However, Amelia experiences a panic attack, prompting her to exit the carriage, despite Antonia's attempts to dissuade her from participating in the balloon launch. Meanwhile, the aspiring meteorologist James Glaisher, embodied by Eddie Redmayne, waits anxiously alongside his friend John, portrayed by Himesh Patel, along with a throng of spectators eager for the balloon launch.
Amelia eventually arrives as the balloon's pilot, making a grand entrance that stuns the crowd, much to the dissatisfaction of the reserved Glaisher. Haunted by memories of her late husband Pierre, played by Vincent Perez, Amelia remains resolute, and the thrilling balloon launch commences.
In a flashback, we see James attempting to present his groundbreaking weather prediction theory at the Royal Society, only to be met with laughter and scorn, especially from Charles Green. Returning home, he faces pressure from his parents to consider a different scientific path. Once in the balloon, James and Amelia ascend through the clouds, reaching 5,450 feet within just over nine minutes. Although they initially revel in the experience, they soon encounter a fierce storm that spins their balloon perilously.
Flashbacks reveal Amelia’s past interactions with James, including a society function where they danced, with Amelia initially annoyed that James only sought her company to recruit her as his pilot. Following a perilous encounter, they continue to rise, but during their ascent, James releases messages through pigeons indicating their altitude and scientific results—just in case disaster strikes.
As they soar higher, James and Amelia bond, enjoying one another's company while James begins to set aside his scientific worries. They discover a current filled with butterflies, lending credence to John's theories that James once dismissed. In another flashback, when Amelia hesitates to fly, James is dismayed but later, after his father expresses pride in him, he regains determination.
The balloon eventually exceeds an altitude of 23,000 feet, breaking records. However, as temperatures plummet, Amelia realizes James did not pack enough suitable attire for the cold and suggests they descend. Their disagreement intensifies, but she ultimately agrees to continue climbing. As they reach 26,500 feet, with dangerously low temperatures, tension escalates when James, under the strain of hypoxia, insists they keep ascending against Amelia's will.
After a heated argument where James invokes Pierre's name—suggesting Amelia’s late husband sought fame at her expense—Amelia retorts that she was the ambitious one. She recounts how Pierre heroically saved her during a critical balloon flight. This revelation brings James back to his senses, leading him to agree to descend. As they face the peril of a frozen gas release valve, Amelia bravely navigates the treacherous exterior of the balloon to rectify the issue, eventually losing consciousness but fortunately tethered to safety.
Upon awakening, she successfully rouses James as they descend amidst swirling snow, realizing their balloon is collapsing from excessive gas loss. They attempt all means to stabilize their descent—ultimately deciding to discard the basket and they cleverly use the balloon as a parachute, cushioning their fall through the trees.
Both emerge from the crash injured yet exhilarated, grateful for their survival. Amelia reflects in a voice-over on how James’ groundbreaking research opened the door for modern weather reporting. The film culminates with James delivering a triumphant presentation at the Royal Society, earning their respect and admiration, concluding with him and Amelia embarking on another balloon adventure together.
