Young Katherine lives in a town of Virgina in 1926. She comes from a black American family and life isn’t easy for them in the South of the United States. Katherine has an innate talent for maths, so her parents will have to move to a different town to give Katherine the opportunity to start a course for gifted students.
Katherine becomes a brilliant mathematician and will find a job at NASA in the Langley Research Group. In 1961, she and her colleagues Dorothy Vaughan and Mary Jackson work as human computers, doing all the math calculations of the complex space operations. However, being a black woman in the 60’s means that they will have to fight really hard to be taken into consideration: they must use a different toilet, drink from different water fountains or eat in “colored” restaurants.
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. She becomes the first black woman on the team and in the building, which has no bathrooms for non-white people.
Her colleagues don’t treat her fairly, especially head engineer Paul Stafford, who will give Karethine enormous load of work to do. Even going to the toilet will be a nightmare if you have to walk for 20 minutes.

Dorothy Vaughan won’t have better opportunities either: she won’t be promoted to a supervisor in spite of her brilliant experience. Mary Jackson has a better luck working with Holocaust survivor Karl Zielinsky, who is the engineer building the space capsule of a rocket. Mary’s suggestions to improve the capsule will earn the acceptance of her colleagues and she even will get encouraged to try to get into the engineer college program, reserved for white men only. Her husband, Levi Jackson, finds it unusual, but he will support his wife pursuing her dream.

One day, at a church barbeque, Mary and Dorothy will introduce Katherine to Colonel Jim Johnson. Katherine is a widow with three daughters, and she will find good help with the company of the Colonel at home.

Al Harrison will also be impressed with Katherine’s solution of a complex mathematical equation. After that, the three women will meet the astronauts of the Mercury 7 mission, and astronaut John Glenn will be particularly kind to the mathematicians.

Meanwhile, IBM computers will be introduced in NASA and will replace a lot of the women who do the calculations. Dorothy learns about this and will teach herself how to use the computer. She will also go to the library and will steal a book from the white-only area of the library. This FORTRAN book is about the programming language of the IBM computer. If Dorothy succeeds in mastering the use of the computer she will be able to teach her team of West Area co-workers.

Dorothy, Katherine and Mary will have to fight hard to survive in a world of white male dominance, with the space race going on and the introduction of technology in everyday life. Will they stop being hidden figures in the eyes of American society?