(CNN) Some movies rely on a single character to make a compelling experience. "Hidden Figures" has three key characters who could make any other movie on their own. So despite an overly calculated feel, the numbers add up in favor of this uplifting film, which celebrates America's pioneer spirit during the space race while delving into that era's shameful aspects vis-à-vis race and gender.

"Hidden Figures" is periodically guilty of a sort of thudding earnestness, as well as emotional manipulation. Still, with its top-flight cast and absorbing historical foundation, the movie doesn't just chronicle when America began reaching for the stars, but sporadically achieves cinematic liftoff.

Starring Taraji P. Henson, Octavia Spencer and Janelle Monae, the film deals with real-life African-American women who played vital roles in the space program back in NASA's "The Right Stuff" days, when John Glenn (Glen Powell) orbited the Earth and the virtues of competing with the Soviets weren't a subject of debate.

Yet while Katherine G. Johnson (Henson) was such a math genius that Glenn requested she crunch the data for his famous Mercury 7 flight, the atmosphere at NASA headquarters circa 1962 was such that Johnson had to walk a long distance just to find a "colored" restroom. This eventually prompts her crusty boss (played with world-weary authority by Kevin Costner) to inquire why she disappears for stretches, prompting her to explain the indignity in a rare outburst.

Katherine's capable supervisor, Dorothy Vaughan (Spencer), is similarly denied a promotion to the job she's already doing by her snooty supervisor (Kirsten Dunst). Meanwhile, Mary Jackson (Monae, having a very big transition-to-acting year with "Moonlight" and now this) yearns to become an engineer, despite some serious impediments due to Jim Crow segregation.

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