Correction: Earlier versions of this article misspelled the last names of David Sabel, the digital producer of London’s National Theatre, and Darryl Schaffer, an executive at Screenvision. This version has been corrected.

When the HD cinecast of “Memphis” hits movie screens for four screenings starting Thursday, it could signal a breakthrough for the theater world.

“Memphis” is last year’s Best Musical Tony winner, it’s still going strong on Broadway and a national tour is on the way — yet for $20 you will be able to catch the Broadway show in your local cineplex.

That’s new, yet “Memphis” has company in the sudden race to convert live theater to limited-run moviehouse experiences. Two weeks ago, the New York Philharmonic’s benefit performances of Stephen Sondheim’s “Company” were “captured” for HD cinecast starting June 15. Neil Patrick Harris stars, and the cast includes Patti LuPone (beloved by Broadway buffs) as well as Jon Cryer and Stephen Colbert (box-office bait from TV).

June will also mark the international HD cinema release of Oscar Wilde’s comic masterpiece “The Importance of Being Earnest,” as it is currently being staged by the Roundabout Theatre Company on Broadway. Roundabout managing director Harold Wolpert suggests that “Earnest” — featuring an acclaimed turn in drag by Brian Bedford as Wilde’s famous society scold, Lady Bracknell — will be the first American nonprofit troupe’s show to get high-def treatment.

That distinction may not last long.

“There’s a lot coming,” says Julie Borchard-Young, whose BY Experience captured “Earnest” and will distribute it to cinemas.

“It’s just starting to snowball,” says Darryl Schaffer, whose Screenvision is distributing “Company.”

But is there any money in it? “I don’t know,” laughs veteran producer Ellen M. Krass, who has brought a number of Sondheim projects to the small screen on PBS. “Call me in a couple months.”

“We’re still in the early stages,” says Bruce Brandwen, whose Broadway Worldwide is behind “Memphis” HD.

The results are already in at the Metropolitan Opera, of course, which these theater dreamers almost universally cite as their model. Next fall the Met will begin a sixth season of its trailblazing “Live in HD” cinecasts, which transmit certain Saturday afternoon performances live from New York to movie theaters around the world. (Delayed screenings and encores are part of the package, too.) Last season “Live in HD” grossed $48 million, according to the Met’s Web site. Half went back to the Met to cover costs and disbursements, and $8 million was profit.

Theater has been following suit most consistently in London, where the National Theatre is completing its second season of “NT Live.” The National’s satellite HD cinecasts are shown in Washington at the Shakespeare Theatre Company’s Harman Center, and the programming has been a hit. Shakespeare’s March screening of the Danny Boyle-directed “Frankenstein” sold out at the 774-seat theater. Two screenings were offered Saturday; one was sold out at presstime. Managing director Chris Jennings bought a large screen as soon as the series began; now he has invested in an HD projector, too.

Technology gets cheaper and better all the time, and such low-end stuff as cell phones used by rabid fans to upload bootlegs has nudged a skeptical and heavily unionized theater industry toward a controlled embrace of digital opportunities. Getting support from the unions has been key, naturally.

One common fear had to do with cannibalization, the concern that video would kill the stage show. But movie versions of Broadway hits “Chicago,” “Rent” and “Phantom of the Opera” didn’t hurt the theatrical box office.

“If you like something, you’re going to see it in multiple formats,” says Brandwen. “Disney has taught us that.”

The cost to capture a performance varies dramatically, depending on which side of the ocean you’re on. Brandwen says it takes $2 million to $4 million; Krass says $1 million to $1.5 million, adding that a one-off like “Company” is easier than a running, fully produced show such as “Memphis.”

In London, the union issues are less knotty and the not-for-profit structure helps, notes the National’s digital producer, David Sabel. The National has set up an in-house unit to shoot the productions it selects for HD, which helps control costs.

The National’s artistic director, Nicholas Hytner, and Sabel take a more aggressive approach to filming than the standard of keeping the cameras hidden.

The National builds platforms, uses cranes and maps out tracking shots, using about a half dozen cameras. Two rehearsals are dedicated just to shooting.

Typically, all these transmissions get downloaded to DVRs, though sometimes the distribution comes on Blu-ray discs or hard-drive files. For the non-live events — Met and NT encores — the exhibitors are licensed to screen the performances a set number of times. Ticket revenue is typically split, though it’s too early for industry standards to be firm. And while Sabel — who is from Bethesda, incidentally — says “this is never going to be a huge money spinner” for the National, he adds that there has been “a small profit on some broadcasts.”

Sabel, like everyone else, cautions that these HD experiences are exciting but no substitute for the real thing. The Met has endured criticism that the cinema phenomenon is tempting the company to design its rep, cast its singers and stage its productions with camera in mind. Can performing arts events conceived for the screen be far off?

“It’s already happening,” says Krass, whose “Company” nearly fits that bill. (The Philharmonic benefit notion came first, Krass says, with the HD idea close behind, and the performers knew about it as they signed on.)

Krass is in talks with companies about potential projects for stage and screen, but while the Met and the National have built-in audiences, it’s not clear what else might excite the masses.

“Does somebody go in to see a Tony-winning play,” Krass asks, “or to see Neil Patrick Harris and Stephen Colbert? I don’t know. We’re on a learning curve . . . I do feel you need a star to get you in the theater, or a Tony-winning piece, or a once-in-a-lifetime event. It’s just not a regular thing.”

Borchard-Young agrees that high-def has opened up a new entertainment niche. “Movies are leaps and bounds ahead in delivering that crisp, clean quality and larger-than-life experience that make these events pop out,” she says. But she adds, “This is not a substitute experience. It’s an additive one . . . We believe in leaving your home and being an active consumer and sitting next to people who are like-minded in that way.”

Says Sabel: “We all live in a world of iPad, streaming, on-demand. Why shouldn’t the arts be able to experiment with that and be innovative?”