Note: The material that follows — presented in the present tense — was gathered from several sources, including Wikipedia and IMBDatabase.

In 1961, mathematician Katherine Goble works as a human computer in the segregated division West Area Computers of the Langley Research Center in Hampton, Virginia, alongside her colleagues, aspiring engineer Mary Jackson and their unofficial acting-supervisor Dorothy Vaughan. Following the successful Soviet launch of Yuri Gagarin, pressure to send American astronauts into space increases.

Supervisor Vivian Mitchell assigns Katherine to assist Al Harrison’s Space Task Group, given her skills in analytic geometry. She becomes the first black woman on the team. Katherine’s new colleagues are initially dismissive and demeaning, especially head engineer Paul Stafford. Meanwhile, Mitchell informs Dorothy that she will not be promoted, as there are no plans to assign a “permanent supervisor for the colored group”. Mary is assigned to the space capsule heat shield team, and immediately identifies a flaw.

With encouragement from the team leader, a Polish-Jewish Holocaust survivor, she submits an application for an official NASA engineer position and begins to pursue an engineering degree. Katherine meets National Guard Lt. Col. Jim Johnson at a barbecue, but she is disappointed when he voices skepticism about women’s mathematical abilities. He later apologizes, and begins spending time with Katherine and her three daughters. When Harrison invites his subordinates to solve a complex mathematical equation, Katherine develops the solution, leaving him impressed. The Mercury 7 astronauts visit Langley and astronaut John Glenn is cordial to the West Area Computers.

Harrison is enraged when he finds out that Katherine is forced to walk a half-mile (800 meters) to another building to use the colored people’s bathroom. Harrison abolishes bathroom segregation, knocking down the “Colored Bathroom” sign. Harrison allows Katherine to be included in their meetings, in which she creates an equation to guide the space capsule during re-entry. Despite this, Katherine is forced to remove her name from the reports, which are credited solely to Stafford. Meanwhile, Mary goes to court and convinces the judge to grant her permission to attend night classes in an all-white school to obtain her engineering degree.Dorothy learns of the impending installation of an IBM 7090 electronic computer that could replace human computers. She visits the computer room to learn about it, and successfully starts the machine.

Later, she visits a public library, where the librarian scolds her for visiting the whites-only section, to borrow a book about Fortran. After teaching herself programming and training her West Area co-workers, she is officially promoted to supervise the Programming Department, bringing 30 of her co-workers with her. Mitchell eventually addresses Dorothy as “Mrs. Vaughan,” indicating her new-found respect.As the final arrangements for John Glenn’s launch are made, Katherine is reassigned back to West Area Computers.

As a wedding and farewell gift from her colleagues (Katherine is now married to Jim Johnson), Katherine is given a pearl necklace, the only jewelry allowed under the dress code.The day of the launch, discrepancies arise in the IBM 7090 calculations for the capsule’s landing coordinates, and Astronaut Glenn requests that Katherine be called in to check them. She quickly does so, only to have the door slammed in her face after delivering the results to the control room.

However, Harrison gives her a security pass so they can relay the results to Glenn together. Stafford, showing a change of heart, brings Katherine a cup of coffee.After a successful launch and orbit, the space capsule has a heat shield problem. Mission control decides to land it after three orbits instead of seven. Katherine suggests that they leave the retro-rocket attached to heat shield for reentry. The instructions prove correct, and Friendship 7 successfully lands.

Following the mission, the mathematicians are laid off and ultimately replaced by electronic computers. Katherine is reassigned to the Analysis and Computation Division, Dorothy continues to supervise the Programming Department, and Mary obtains her engineering degree and gains employment at NASA as an engineer.An epilogue reveals that Katherine calculated the trajectories for the Apollo 11 and Space Shuttle missions. In 2015 she was awarded the Presidential Medal of Freedom. The following year, NASA dedicated the Langley Research Center’s Katherine G. Johnson Computational Building in her honor.