In the midst of the Space Race of the 1960s, three African American women work as mathematicians at NASA’s segregated West Area Computers division in Langley, Virginia. These women are faced with the dual challenges of gender and racial discrimination in a predominantly white, male-dominated workplace. Katherine Johnson is a brilliant geometrician assigned to the all-male Space Task Group, where her mathematical skills contribute to the project's crucial calculations. She faces both the arduous work of calculating launch trajectories for America's first orbital flights and the everyday slights of segregation, having to sprint half a mile to use the “colored” bathroom.

Meanwhile, Dorothy Vaughan realizes that the installation of an IBM computer could render her current role obsolete. In response, she takes it upon herself to learn the programming language Fortran, seeking to ensure her and her team's relevance in the evolving space industry. At the same time, Mary Jackson, a talented engineer, confronts legal barriers to her advancement; she seeks to become NASA’s first black female engineer and must petition the court for the right to attend all-white evening classes at a segregated high school to further her education. Together, these three women persist against the societal norms of the day, playing pivotal roles in the efforts to put an American astronaut into orbit, an achievement that would restore the nation's confidence and turn the tide of the Cold War.