With Tony winner “Memphis” skedding four special-event cinema screenings of the tuner and Beatles tribute “Rain” set for a couple of encores on public television, Broadway is increasingly seeing the value of getting a stage project onto screens while the live show is still on the boards.

The spate of Broadway-originated cinemacasts, which also includes a recently announced movie-theater broadcast of “The Important of Being Earnest,” reps a sea change from past years, when producers believed a full-length filmed version of a show would cannibalize biz from the Main Stem original.

Producers these days seem far more likely to screen incarnations as valuable marketing and branding opportunities.

“Memphis” — recorded live in HD over a couple of performances in January — will hit screens in a presentation from digital alternative-programming distributor NCM Fathom and Broadway Worldwide.

Skedded for April 28 and 30, May 1 and 3, the perfs are skedded to piggyback off the national spotlight that turns on Broadway during the runup to the Tony nominations, to be announced on May 3.

To take advantage of student-group biz, they’re also skedded when schools will still be in session, and prior to the summer onslaught of attention-hogging Hollywood tentpoles.

According to Fathom veep Dan Diamond, performing arts programming, including the regular series of HD cinemacasts from the Metropolitan Opera, has proven among the most popular offerings for Fathom.

“We get asked more and more for that type of programming,” Diamond said.

For producers of “Memphis,” the screenings in 530 theaters around the country expose the show to the kind of broader national audience that keeps longrunning productions afloat.

Move also boosts the profile of a title that doesn’t benefit from the instant familiarity of a well-known property such as “The Addams Family.”

In general, such screenings also help pump up the international reach of production orgs including the Met and, with an unrelated series of cinemacasts, London’s National Theater.

Meanwhile, fab-faux Beatles concert “Rain,” which played on public TV in August, will re-air the special presentation twice, Saturday and Sunday, on metro area public television station WLIW. Broadcasts will remind area theatergoers of the show now that it’s resumed performances following a limited run that proved popular enough to warrant a longer stint at another theater.

The demise of the stage production of “Annie,” six months after the release of the 1983 film, was for years cited as a favorite example of how a screen version could kill a stage original.

But legiters’ new attitude toward screen versions comes in part from the noticeable upticks seen in Broadway B.O. when more recent film adaptations of musicals hit theaters. Releases of movie-tuners including “Chicago,” “Rent” and “The Phantom of the Opera” all helped revitalize sales for the stage productions that inspired them, even when the resulting movie wasn’t particularly well-received.

The thinking is that the brand-building benefits of a movie version lends a valuable familiarity to a show on Broadway, where always-increasing ticket prices can encourage theatergoers to gravitate to pre-approved fare.

In 2007, “Legally Blonde” took the unusual step of filming the show for broadcast a handful of times of MTV. Targeting a young, female demo through the choice of network, the move aimed not just to boost the profile of “Blonde” as a Broadway stage property but also to stir national audience interest in an outgoing tour.