At a San Diego military air station, McVey, a young sailor, is scheduled to fly to Washington, D.C., on a jet piloted by Capt. Dale Heath, who was involved in a mid-air collision three years earlier. Meanwhile, at the Heath residence, Dale’s philandering wife Cheryl smugly tells Dale that she seduced him to destroy his grounds for divorce, because her lawyer advised that consenting to sex after catching one’s partner in flagrante delicto legally implies forgiveness. Wearily, Dale tells Cheryl that he is not planning to renounce his marriage vows and is more concerned about their daughter, Anne, who wants to go to boarding school to get away from her mother. After bribing Cheryl with a new convertible, Dale tells the adoring Anne that she can pick out a school to attend. Later, at the airfield, Dale explains to McVey that they will be flying under Instrument Flight Rules, which, to avoid head-on collisions, dictate that eastbound planes fly at odd-numbered altitudes and westbound, even-numbered, leaving 1,000 feet of airspace between their paths. When McVey asks about his collision, Dale, a Korean War veteran, explains how an off-course B-66 heading toward him momentarily awakened his wartime instincts, causing him to fly evasively upward. Although he was able to eject from his cabin, his survival was at the expense of the other plane, which crashed into his plane’s belly and trapped its occupants. In a Washington, D.C. taxi, stewardess Kitty Foster and her boyfriend, pilot Mike Rule, whose passion is painting, are heading to the airport to serve on a Trans States Airline flight to Los Angeles. Kitty asks Mike to marry her, but he is distracted by one of his drawings that has been bought by a cigarette company to use for an ad. At the airport Dick Barnett, who will head the westbound crew, turns down a promotion to a desk job offered by airline executive J. B. After the passengers board, Dick takes off and settles into a flight path at 20,000 feet. Despite tension between them, Mike asks about Dick’s son, Dick, Jr., which causes Dick tacitly to reminisce about his child: Although Dick wants the baby named after him, later he and his son never get along, as Dick is a stern father who is quick to criticize and slow to compliment. When his wife Bev dies, his son finds no comfort from Dick’s stoic demeanor, and instead cries on family friend Mike’s shoulder. Dick’s perfectionist attitude further alienates his son, who, as a teenager, is arrested for a prank. In the present, Dick recalls Bev saying that he cannot understand his son, because he never makes mistakes. She explains, “Without mistakes, there is no forgiving, and without forgiving, there is no love.” Mike interrupts Dick’s reverie to point out that he is flying five hundred feet too high, but Dick, resenting criticism, claims he is flying above the turbulence for the comfort of the passengers and is contemptuous of Mike’s argument about “the crowded sky.” Flying east, Dale and McVey experience severe weather conditions and discover their radio is out of order, rendering communication with the air traffic control centers impossible. After trying to distract McVey from his anxiety, Dale thinks about his final days at the Naval Academy: Cheryl, a rear admiral’s daughter, tricks him into marriage immediately after graduation by falsely claiming she is pregnant. After he refuses to accept preferential treatment by her father and is assigned to a Truth or Consequences, New Mexico, airfield, she begins having affairs. In the present, Dale concedes to himself that, without his unhappy marriage, he would not have Anne. In the westbound plane, Kitty asks Mike about the tension between him and Dick, causing Mike to remember events from the past: At a poker game, Mike’s senior officers announce that he is ready to be a captain, but Dick disagrees, saying that Mike cannot be devoted to both flying and painting. Having his promotion officially blocked by Dick, Mike gets drunk and awakens the next day in Kitty's apartment. They have never met before, but she owns one of his paintings and has read about his deceased father Noah, a tormented but famous painter who burned all but four of his creations. Attracted to Kitty, Mike borrows a Cessna and flies her to see Noah’s extant works, but warns her that he intends to stay unmarried and without children, so he can pursue his art. Kitty says that she is uninterested in an affair, and later confides that years earlier she bore a child, whom she was forced to give up. While viewing a painting of Noah’s that is owned by one of the artist’s many former wives, Mike, to his surprise, learns that his father is alive and living in an asylum. After they visit Noah, Kitty says that she has fallen in love with Mike and believes that they may someday marry. When Mike's thoughts return to the present, the plane is almost halfway across the continent. He again insists that Dick fly at the correct altitude, but Dick stubbornly refuses. Dale and McVey land in El Paso to have the radio repaired and then take off again. In the air, the radio again malfunctions, preventing Dale from sending calls, although he can receive them. Because he is unable to ask for an altimeter setting, he cannot ascertain that he is flying too low. Following standard procedure, he continues on course to avoid collision, but, as a signal to the control center, flicks his IFF switch, alerting a quick-thinking controller below who guesses his problem. When the controller radios a warning that Dale appears to have dropped 1,000 feet too low, Dale flies his jet upward. Above them, at Mike’s urging, Dick descends, aiming for an altitude of 2,500 feet, unaware that he is on a collision course with Dale’s plane. When Dale spots the plane heading toward him, he instantly chooses to sacrifice his plane for theirs and dives. The planes collide and, seconds later, the jet explodes. In the collision, Dick’s plane loses one engine and his flight engineer is sucked out of the plane to his death while Kitty and another stewardess assist the frightened and injured passengers. With one wing on fire, Dick skillfully makes an emergency landing, saving most of his crew and passengers, and afterward, at a hearing, claims full responsibility for the crash, which, he explains, was due to his own “pilot error” coinciding with Dale’s plane’s mechanical failure. After acknowledging his own shortcomings, Dick is able to reunite with Dick, Jr. Later, Mike proposes to Kitty in front of a billboard featuring his painting.