Behold a Broadway musical that sings, dances and bedazzles so magnetically, it feels as if it were ordained for the screen by divine providence. “Roald Dahl’s Matilda: The Musical” certainly is divine, but the inspirational figures are all mortal: a director, Matthew Warchus; a star, Emma Thompson; and a cast of perpetually whirling child wonders who propel the story forward with kinetic enchantment.

“Matilda” was first a Dahl novel, then a 1996 movie, then a 2013 Broadway musical and now a movie musical. Audiences have seen countless times how this progression can devolve from one incarnation to the next, as if a property were subject to imaginative biodegrading. In this instance, the opposite pertains: “Matilda,” in select theaters now and streaming on Netflix beginning Christmas Day, explodes with an exhilarating pleasure in filmic transformation, in harnessing the strength of one medium and regenerating it freshly in another.

The movie reassembles key members of the stage version’s creative team, including book writer (now screenwriter) Dennis Kelly and composer Tim Minchin, under the guidance once again of Warchus, a Broadway and West End veteran. Their cinematic take is by some magnitude even more faithful to Dahl’s dark vision of childhood terrors, as it unfolds a harsher depiction of the plight of Matilda (the astonishing Alisha Weir). And it counts even more pointedly than the stage adaptation did on our reflexive sympathy for children subjected to the dictatorial whims of cruel adults.

At the heart of it all is Thompson as heartless Agatha Trunchbull, authoritarian headmistress of Crunchem Hall, a primary school over which she presides with Olympian contempt for terrorized pupils she calls “maggots.” Thompson is a lover of elaborate dress-up – recall, please, “Nanny McPhee” – and here she’s bulked up and uniformed like a totalitarian despot. Hers is a megalomaniacal tour de force that reaches its climax in the extraordinary “The Smell of Rebellion,” a musical rampage on a muddy obstacle course that passes for a grueling phys ed class.

Ellen Kane is the choreographer for this and other remarkable production numbers – she was Peter Darling’s choreography associate for Broadway – that have you marveling at what can be achieved with a legion of nimble tweeners. Think of “Oliver!” with 10 times the combustion. In songs such as the welcome-to-hell “School Song” and “Bruce,” recounting a penitential cake-eating challenge, the ensemble dances through the hallways and assembly rooms with dizzying élan.

“Matilda’s” guiding principle is that adults may indulge in self-satisfying fantasies about their little darlings: “My mommy says I’m a miracle,” sings the opening number, as cinematographer Tat Radcliffe pans over adorable newborns in their cribs. But once they’re old enough for school – well, maybe that’s when moms and dads should be paying closer attention. Crunchem Hall is “Nicholas Nickleby’s” Dotheboys Hall with an extra soupcon of sadism. (Although Miss Trunchbull inflicts physical punishment that magically results in no lasting harm, I’d say the movie is not for youngsters who can’t yet distinguish between real and pretend.)

As opposed to J.K. Rowling’s Hogwarts, Crunchem Hall is a perverse sendup of the brutalities of the British school system. Matilda Wormwood’s home life is just as awful, as it is presided over by cartoonishly self-centered parents (played expertly by Stephen Graham and Andrea Riseborough) who are oblivious to what is apparent to the rest of us: that Matilda is a wondrous child with supernatural gifts and brain power to spare. That is left to be discovered by the story’s most benevolent character: Matilda’s schoolteacher Miss Honey, embodied with heart-melting wholesomeness by Lashana Lynch.

The Wormwoods have been stripped in the film version of most of their singing responsibilities – there was no way, apparently, to make one of the musical’s funniest songs, Mr. Wormwood’s audience-participation “Telly,” work for the screen, and Matilda’s brother Michael has been cut out entirely. Young Weir’s luminous presence more than compensates for anything that has been subtracted. Her endearing Matilda is equal parts dreamer and rebel, attributes documented brightly in the Necco-Wafer-colored world conjured by production designers David Hindle and Christian Huband.

The other besieged children gallivant just as vivaciously, among them Charlie Hodson-Prior as Bruce, Winter Jarrett-Glasspool as Amanda and Rei Yamauchi Fulker as Lavender. When a show opens up so buoyantly for the cameras, it is most definitely a happy holiday.