BASED ON A TRUE STORY
The film opens in White Sulphur Springs, West Virginia in 1926. A young Katherine Coleman (
Lidya Jewett) is waiting, naming the geometric shapes in a stained glass window, while her parents talk to a school official. The official wants to sent Katherine to a school for gifted students -- she's an advanced student and a genius at math. The only such school for "colored" students starts at the sixth grade and Katherine is only eight, so she will have to skip several grades. That worries her parents, but they agree it will be best for her, even though the family will have to move. Katherine's teacher gives her parents some money to help with the move, from a collection all the teachers contributed to.
At the new school, a teacher asks Katherine to tackle an algebra problem on the blackboard; the camera zooms in on the teacher's hand as he passes Katherine the chalk. Katherine solves the problem without hesitation, then turns around and explains it to her teenaged classmates.
In Hampton, Virginia, in 1961, an adult Katherine (
Taraji P. Henson), now Katherine Goble, is stuck on the side of the road with the two co-workers she carpools with, Dorothy Vaughan (
Octavia Spencer) and Mary Jackson (
Janelle Monáe). A racist police officer stops and asks for identification. When they explain that they work at NASA, he changes his tune; he's surprised they hire black women, but he's impressed. He seems very well-versed in NASA and asserts that the Americans have to beat the Russians in the Space Race. He asks if they've met the astronauts; Mary answers that they have but it's clear from the others' expressions that they're kept separate from them. Dorothy manages to get the car up and running and the police officer provides them an escort -- lights and sirens blazing -- to the NASA Langley Research Center, which they find ironic since it's not usually a group of black people speeding to follow a police car.
The Space Task Group watches a newsreel about Russia's launch of Sputnik 1, the first artificial satellite. In the ensuing discussion, leaders worry that the Soviets' access to space could allow them to spy on America. The man in charge demands that Al Harrison (
Kevin Costner) get them up there because they can't justify the cost of a space program that doesn't put anyone in space. A man in the crowd, Paul Stafford (
Jim Parsons), makes a snooty comment and is asked what his position is. He explains he is the head engineer.
The three women work at the West Area Computing division, segregated from the rest of Langley Research Center, along with many other black women who work as computers -- meaning they do math by hand. Dorothy gives out new assignments to the group. Mary wants to work as an engineer but she is told she is going to be assisting the male engineers. Vivian Mitchell (
Kirsten Dunst), Dorothy's boss, comes in to talk to Dorothy. She tells her the Space Task Group needs a new computer who can do analytic geometry. Dorothy assigns Katherine because she knows analytic geometry and she's the all-around best at numbers.
Vivian (whom the black women all address as Mrs. Mitchell, though she calls them by their first names) escorts Katherine to the Flight Research Division elsewhere on the campus, telling her that the dress code for women is skirts below the knee and no jewelry except maybe pearls. She tells Katherine the department she's joining is demanding and has dismissed several computers lately; she doesn't expect Katherine to last long. She warns her not to speak to the department head, Mr. Harrison, unless he speaks to her first. Vivian notes that they've never had a colored person in that department and admonishes Katherine not to embarrass her. Katherine enters the large area where white men are working, some at desks and some at equations on blackboards so tall they need ladders. Mr. Harrison's glass-walled office overlooks the work area. Katherine is mistaken for a janitor and the men act rudely towards her.
In the engineering department, Mary carries her papers through a sealed chamber where a space capsule is about to undergo wind tunnel testing; she stops to admire it. As the test countdown nears zero, the heel of her shoe gets caught in a grate on the floor and she can't pry it loose. The male engineers in the observation room shout that her life is not worth a shoe so she abandons it and joins the engineers behind the glass. The space capsule fails the wind test -- many of its louvered exterior heat shielding panels fly off. Mary and the engineers examine it and the head engineer, Karl Zielinski (
Olek Krupa), muses that they could use a corrugated heat shield. Mary suggests that they try different fasteners for the existing panels instead. Zielinski says she ought to be an engineer, and she says that she's a negro woman, and she's "not gonna entertain the impossible." He asks, if she was a white man, would she wish to be an engineer? She responds that she wouldn't have to; she'd already be one. Mary explains that the only schools that have the programs needed to become an engineer are off limits to colored people.
Dorothy asks Vivian if she can be promoted to supervisor since she's doing the work of a supervisor already. But Vivian refuses -- claiming it's not her call -- which Dorothy has to remain diplomatic about because she's not in a position to debate. Meanwhile, Katherine is given a lot of work to check by Paul Stafford, who is short with her, telling her his numbers are perfect and he needs them checked by the end of the day. He has also blacked out a lot of information as if Katherine couldn't be trusted with it. She has to hold it up to the light to read it because she can't solve the problems otherwise.
Time passes and Katherine needs to use the restroom. She asks Ruth (
Kimberly Quinn), who's white and the only other woman in the department, where it is and is told, "I don't know where YOUR bathroom is." Katherine goes outside, needing to pee, but realizes the bathroom in that building is for white women only and can't sneak in because some white women are loitering nearby. She has to leave the building and run half a mile to the colored women's bathroom in the West Area Computing division she used to work in. She brings her work with her and continues to proof it while she pees.
That night, Dorothy is in a bad mood as she drives the other two home, complaining about Vivian not making her a supervisor when she's been working as one for years. Katherine gets home and finds her three daughters fighting in their bedroom. (It turns out Katherine is a widow, and her mother takes care of her children while she works.) The young ones want to know why the oldest one gets her own bed. Katherine says if they want to take on the same chores and responsibilities, they can earn the right to the bed. The younger girls agree they are fine sharing. They complain that their mom has been gone for a long time and she cites her new position as the cause.
The three women go to church with their families and a handsome colonel (
Mahershala Ali) catches Katherine's eye. At the barbecue afterwards, Mary signals for the man, Jim Johnson, to come over and talk to Katherine. He does, and Dorothy and Mary make themselves scarce. Jim and Katherine flirt with each other, but he gets off on the wrong foot when he hears about her work at NASA, expressing surprise that they "let women" do something "so taxing." She tells him off and marches away.
Back at NASA, Katherine pours herself a cup of coffee, which unnerves all the white people in the Space Task Group -- in segregated Virginia, white and colored people don't usually drink from the same pot. Nobody says anything, but the next day when Katherine looks for coffee she finds a separate pot labeled "Colored."
Al Harrison joins the group and asks if anyone wants to take a crack at an equation on a large chalkboard that has gone unsolved. Nobody notices but Katherine steps up and does the math. Time passes and Al asks who solved the problem. When Katherine admits she did, he asks what she does and Katherine tells him she is checking work. She shows him and he asks how she's able to work with all the blacked out sections. She demonstrates that you can read the blacked-out text if you hold the paper up to the light. She requests that she get uncensored reports in the future. Al agrees, saying that she's not a Russian spy so there's no reason to keep information from her. Stafford, who is in Harrison's office during this exchange, is chagrined.
The NASA employees are gathered out on the launch site to meet the astronauts, including John Glenn (
Glen Powell). Glen will later pilot the Friendship 7, becoming the first American in orbit. He is discouraged from greeting the black women, who are standing apart from the white employees, but he comes over anyway and proves to be friendly.
Katherine is assigned to write up reports and, because the majority of the research is hers, puts her name on the byline after Paul Stafford's. When Stafford sees it, he makes her retype the cover sheet without her name because computers aren't allowed to author reports.
On a rainy day, Katherine sprints the long distance to use the colored women's rest room. Al Harrison comes to her desk looking for her, but -- not for the first time -- she's missing. When she returns, Harrison asks her why she is gone for so long every day. Soaking wet, Katherine launches into a tirade about how she has to run half a mile to the west campus to use the colored women's rest room because there's no toilet she's allowed to use in the building they're working in. She adds that she's not allowed to drink coffee from the same pot as everyone else and she's been forbidden to wear any jewelry other than pearls, but she's never owned any -- NASA doesn't pay colored computers enough to afford pearls. Al listens closely. He doesn't say anything, but after Katherine storms out, he walks over to the coffee station and rips the "Colored" label off her coffee pot. In the next scene, a crowd watches as Al attacks the COLORED WOMEN bathroom sign in the West Area Computing division with a crowbar. When it falls, he says from now on, there will be no segregation of bathrooms: "Here at NASA, we all pee the same color."
Dorothy has been curious about a large empty room near her office with windows facing the hallway. When she sees that a big digital computer has been installed there, she sneaks in and studies the IBM machine they've set up. Later, she takes her children to the library and finds a book on FORTRAN programming. A white woman spots her and complains she's in the wrong section. Dorothy tells her that they didn't have the book she wanted in the colored section. She is kicked out of the library but reveals that she has taken the book with her. When her son asks her about it, Dorothy says she's a taxpayer and the library is government owned so she's entitled to take the book.
Now Katherine is respected by her white male colleagues. They pour her coffee from the same pot. She writes a report and puts her name on top again. Paul tells her not to do this because computers don't get credited on reports. Katherine debates that it's her math. She also voices to Al Harrison that she wants to be included in meetings about the Friendship 7 launch since she is responsible for updating the launch calculations every time there's a change of any kind -- to the launch time, payload, landing location, etc -- and changes are discussed at almost every meeting. Al points out there's no protocol for women attending meetings but she responds there's no protocol for a man circling the Earth either. He wonders who can change the rules and Katherine points out that he's the boss if he'll just act like one. Despite Paul's protests, Al agrees to let her sit in, saying that they all work together or not at all. But he tells her to keep quiet.
Katherine follows Al into the meeting, which includes John Glenn and a lot of NASA big-wigs. One of them complains to Al that they need a way to figure out where Glenn's Friendship 7 space capsule will land. There's a long silence while Al contemplates the problem. Then he holds out a piece of chalk to Katherine and asks her to take a stab at it. The camera zooms in on the hand-off of the chalk, recreating the scene early in the movie when the teacher asks a much younger Katherine to step up to the blackboard. Katherine isn't prepared for this -- she thought she was there just to listen -- but she thinks it through and covers half the blackboard with a set of equations that predict, based on current plans, that Glenn will splash down at a particular latitude and longitude near the Bahamas. No one can see any flaws in her logic or her numbers, so they're all impressed, including John Glenn.
Mary goes to a judge and asks if she can attend a school that does not allow colored people so she can get a degree in engineering. She is granted permission to enroll exclusively in night classes, making her the first colored woman to attend. She goes to class and the white students are taken aback but it does not bother her.
Dorothy has been reading IBM documentation, brushing up on FORTRAN, and paying secret visits to the IBM computer in the data center. The men tasked with getting the machine working are having a hard time, and Al has threatened not to pay them. Dorothy has also asked some canny questions and discovered that once it proves its reliability, the IBM -- which can run computations many times faster than a whole room full of human computers -- will replace her West Area Computing unit. On one of her visits to the data center, Dorothy notices that one of the cables on the IBM's patch panel is in the wrong place and reconnects it correctly, which fixes the problem the men were having. Dorothy is testing a program on a set of punch cards when the male technicians rush in and ask her what she's doing. They're terrified that she might break something until they realize that Dorothy, puttering around in her spare time on her own, has managed a feat that has eluded them for weeks: she's gotten the computer to run a program and produce meaningful results.
When Vivian notes that they are short on computer programmers, Dorothy reveals that she has become proficient in FORTRAN, and she's been teaching the computers in her group about FORTRAN and the IBM machine. She arranges for all 30 of the women she had been working with to come along and join the staff, citing that they are short on manpower. Dorothy then tells the women that they've all been reassigned and they walk as a group to their new department.
Katherine continues writing reports with John Glenn's launch approaching, eliminating her own name despite reluctance to do so. Al tells her that, now that Friendship 7 is about to be launched, the Space Task Group's need for Katherine has ended. Everyone in the group has come to value her and as she packs up her things, Ruth gives Katherine a wedding gift from the whole group: a string of pearls.
The day of John Glenn's launch, Vivian runs into Dorothy in the bathroom. She apologizes to Dorothy for never making her supervisor. Vivian tells Dorothy she has nothing against the black women under her supervision and always did the best she could for them. Before walking out, Dorothy studies her and says pityingly, "I know you really believe that."
The whole world tunes in to watch John Glenn's launch. Katherine is in the research department, alone, when a problem arises in the control center the electronic computers calculations for Johns flight do not match a previous days, so they don't know which coordinates to set for the launch and landing of the orbit. John requests that Katherine do the math by hand because shes smart. Al is able to locate her and she is escorted into her old Computers office. She works on the equation until finally verifying which one is right. She revels in the achievement and then realizes she has to convey that information to John Glenn so he can launch as scheduled. She is raced back to the control center and the notebook is handed to Al, who is inside. The door is shut on Katherine, who stands outside, dejected, despite saving the day. A moment passes and then Al returns, ushering her inside with him.
Fifty million people watch the liftoff on television while Mary and Al watch from the control center. We see the horizon from the space shuttle as John Glenn sends Friendship 7 into orbit. After successful orbits around Earth, Glenn notices a control problem the heat shield is not locked in position and only held in place by the straps of the retro package. He also complains that the temperature is getting too hot. Mary is watching the TV. She rushes to a payphone and calls NASA, screaming to let the control center know that John should keep the retro pack in place during reentry and retract the periscope manually. This information is relayed and proves correct.
The world is nervous about Johns reentry. He loses altitude and uses the fly-by-wire mode, experiencing peak reentry heating. But then he regains stability and re-enters. Katherine experiences this moment with the rest of the crew.
After the launch, the activity at NASA dies down. Dorothy learns that all the computers are going to be laid off, now that electronic computers are available. But she is kept on in the Research Center's Analysis and Computation Division. Mary gets her degree and becomes an engineer.
Katherine returns home after a long day and Jim Johnson is waiting for her. They have reconciled after their argument and he proposes to her. She accepts.
In post-script, we learn about all three of the women's accomplishments at NASA. Katherine calculated the trajectory for the 1969 Apollo 11 flight to the Moon and on Apollo 13, as well. She was awarded the Presidential Medal of Freedom in 2015. In 2016, the Langley Research Center in Virginia that she worked at was renamed the Katherine G. Johnson Computational Research Facility. She is currently retired and has remained married to Jim Johnson to this day.