We’re in White Sulphur Springs, West Virginia in 1926. A young Katherine Johnson is waiting, naming the geometric shapes on the wall, while her parents talk to a teacher at a school for gifted students. They want Katherine to skip several grades because she is so intellectually advanced and a math genius. We see her as a young girl solving algebra equations that her teenaged classmates can’t.
We jump forward to the 1961 in Virginia where an adult Katherine (Taraji P. Henson) is stuck on the side of the road with her two coworkers that she carpools with -- Dorothy Vaughan (Octavia Spencer) and Mary Jackson (Janelle Monáe). A police officer stops and asks for identification. When they explain that they work at NASA, he changes his tune, vocalizing that he’s surprised they hire black women. He seems very well-versed in NASA and points out that the Americans have to beat the Russians in the Space Race. He asks if they are friends with the astronauts; Mary answers that they are but it’s clear from the other’s 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 to the NASA field 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 has a meeting about how they are going to beat Russia, which has just had success with Sputnik 1, the first artificial satellite. They’re worried that the Soviets having 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 Computers division of the center, segregated from Langley Research Center, along with many other black women who work as “computers,” doing math by hand. Dorothy gives out new assignments to the group Mary wants to work as an engineer but now she is told she is just going to be assisting them. Vivian Jackson (Kirsten Dunst), comes in to talk to Dorothy. She tells her the Space Test Group needs a new computer. Dorothy suggests Katherine because she’s the best at numbers.
Vivian escorts Katherine to the Flight Research Division elsewhere on the campus, telling her that it’s standard for women to wear skirts and no jewelry except maybe pearls. She tells Katherine they’ve never had a colored person in that department and not to embarrass her. Katherine enters the large area where white men are doing math equations. She is mistaken for a janitor and the men act rudely towards her.
In the engineering department, Mary carries her papers through the closed off area where a space shuttle is going to be tested. As it counts down, the heel of her shoe gets caught and she can’t pry it loose. They shout that her life is not worth a shoe so she abandons it and joins the male engineers behind the glass. The space shuttle explodes. They examine it and ask her opinion as to what went wrong. She is able to deduct that the heat shield flew off the shingles and knows what caused this to happen. Mary then explains how it could be corrected which impresses the engineer. He asks, if she was a white man, would she want to be an engineer? She responds that she wouldn’t have to; she’s already be one. Mary tells him 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 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 it 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 a woman 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 women are loitering nearby. She has to leave the building and run half a mile to the West Area Computer 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. 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 and a handsome colonel (Mahershala Ali) catches Katherine’s eye. At the barbecue afterwards, the women signal for the man, Jim Johnson, to come over and talk to Katherine. The two of them flirt with each other.
Back at NASA, Katherine goes to pour herself a cup of coffee, which unnerves all the white people as she is supposed to drink from a separate pot. Al Harrison joins the group and asks if anyone wants to take a crack at a math 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 math 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 admits she holds it up to the light and requests that she get the reports without being blacked out. He agrees, citing that she’s not a Russian spy so there’s no reason to keep information from her.
The NASA employees are gathered out on the launch site to meet John Glenn (Glen Powell) who will be piloting the Friendship 7, which would make him the first American in orbit. He is discouraged from greeting the black women, who are segregated from the white employees, but comes over anyway and proves to be friendly.
Katherine is given the assignment to write up reports and, because the majority of the research is hers, she assigns them to “Paul Stafford and Mary Goble.”
On a rainy day, Katherine sprints the long distance to use the Colored Women’s room. When she returns, Al asks her why she is gone for so long every day. Soaking wet, Katherine launches into a huge speech about how she has to use the Colored Women’s room and how she’s not allowed to drink coffee from the same pot and how she’s been forbidden to wear pearls but she’s never owned any. Al sympathizes with her and goes to the West Area Computer division and knocks down the COLORED WOMEN bathroom sign with a sledgehammer. He says, from now on, there will be no segregation of bathrooms.
Dorothy sneaks into the data processing center 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 hers. 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 claims she’s a taxpayer and the library is government owned so she should be free to take the book.
Katherine sees Jim again at a picnic and he asks what she does for a living. When she tells him she works as a computer at NASA, he voices that he’s surprised that they let women handle that kind of math. Offended, Katherine tells him they don’t judge her by her skirt but by her glasses.
Now Katherine is respected amongst 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 on meetings since she is in charge of analyzing the discussions. Al points out there’s no protocol for women attending meetings but she responds by saying 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 just acts like one. Despite Paul’s protestations, Al agrees to let her sit in, stating that they all work together or not at all.
Katherine attends her first meeting, with John Glenn and his crew. She hears of the latest problem, that they don’t know the no-go of the space shuttle and if they bring him in too soon, he will burn up on re-entry. They have to get the calculations perfect so they know exactly when he needs to return. The problem is the math they need doesn’t exist yet. Katherine is asked to go to the board and work on the problem. She points out that the shuttle will be travelling both in an elliptical and parabolic direction. She comes up with an equation that works, which impresses everyone, including John Glenn.
Mary goes to a judge and asks if she can attend a school that does not allow colored people, allowing her to get a degree in Engineering. She is granted permission to exclusively 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.
When Vivian notes that they are short on computer programmers, Dorothy reveals that she has become proficient in FORTRAN. 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 collectively to their new department.
Katherine continues writing reports with John Glenn’s launch approaching, eliminating her own name despite reluctance to do so. They let her know that, now that Friendship 7 is about to be launched, their need for Katherine has ended. Everyone has come to love her and they give her a gift of pearls as a send-off gift.
The day of John Glenn’s launch, Vivian runs into Dorothy in the bathroom. She apologizes to Dorothy for never making her supervisor and that she never treated her differently because she’s black. Before walking out, Dorothy studies her and pitifully says, “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 computer’s calculations for John’s flight do not match a previous day’s, 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 she’s 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 John’s 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 has remained married to Jim Johnson to this day.
*CUT TO THE CHASE*
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In 1961 Virginia, three black women work at NASA as “computers,” doing math by hand given that they’re all fairly smart and educated. One by one, they work their way up the ranks of the space program. Katherine Goble, a math genius, ends up calculating the math for John Glenn’s spaceflight, which is the first time an American has ever orbited the Earth. Dorothy Vaughan studies FORTRAN programming and becomes a computer programmer. Mary Jackson goes to court to be granted permission to study engineering, which has been off-limits to colored women in the area, and eventually becomes an engineer.
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