In 1961, mathematician Katherine Goble works as a human computer in the gender and racially 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.