“Hidden Figures” is old-fashioned in a good way, classical and well-acted, and that it has no surprises keeps it from being disappointing, even as it keeps it from being great.

It tells the story of three black women who worked at NASA in the very early days of the 1960s, back when the Soviets were outpacing us in the race for the moon. It takes place, not in Houston, but in NASA’s Northern Virginia headquarters, which is important, as this was the South before civil rights.

All three of these real-life women made contributions to American space exploration, but Katherine Johnson, played by Taraji P. Henson, is at the center of the film. A math prodigy from childhood, she was one of a team of people assigned to double check NASA’s mathematical calculations. Gradually, she began to stand out from the pack and assume greater importance, though at the time no one expected genius in the form of a woman, or a black person, or most especially a black woman, so nothing was easy for her.

Dorothy Vaughan (Octavia Spencer) was the leader of a computing team, back when the word “computers” referred to people who did computations. Eventually, she would become an expert in computers as we now know them. And Mary Jackson (Janelle Monae) became an aerospace engineer.

Because it’s based on fact, “Hidden Figures” is not as immediately satisfying as a fictional version of this story might have been. For one thing, the women remain as “hidden figures.” Though they achieve professional respect and security in their positions, people don’t fall over themselves to tell them how right and wonderful they are, and the movie doesn’t overestimate their impact.

Theodore Melfi (“St. Vincent”), who directed and co-wrote the film, based on the book by Margot Lee Shetterly, does a nice job of organizing and telling a complicated story, involving three women and their personal and professional lives. Where the movie lets us down is in the matter of tone. It feels light — at times too light — and so we get a scene of the three women dancing around the house, which is obligatory in all Hollywood movies dealing with female friendship.

More problematic is the recurring scene of Katherine having to run to the bathroom. Apparently, in the division in which Katherine worked, there were no “colored” bathrooms, and so she had to walk (or run) a half mile every time she needed to relieve herself. But the movie underscores these scenes with music suggesting that this situation is comic or at least farcical, when it’s neither.

Kevin Costner is nicely cast as Al Harrison, Katherine’s boss, who is mostly too busy to differentiate the very smart people on his staff from the flat-out geniuses. Costner is a useful actor to have in period films, because he can slip into that mid-century vibe like nobody else. It’s more than just short hair and a white shirt, but rather a whole way of being, an attitude, the life history. In a way, he’s the most authentically 1962 thing in the movie.

MOVIE REVIEW

“Hidden Figures”

Grade: B

Starring Taraji P. Henson, Octavia Spencer, Janelle Monae and Kevin Costner. Directed by Theodore Melfi.

Rated PG for thematic elements and some languages. Check listings for theaters. 2 hours, 7 minutes.

Bottom line: Old-fashioned in a good way, but could use some surprises