Consultant Ryan Barson and his wife, Heather, can identify the moment they knew they’d made the right decision to hold a family reunion aboard a cruise ship.

It was at a Beatles tribute concert on Royal Caribbean’s gigantic Allure of the Seas. In the audience, Heather’s parents, Brent and Becky Fuller, 66 and 65, of Salt Lake City, danced to the music. Meanwhile, the Barsons’ four sons, aged 10 to 18, sang along to “Love Me Do.”

“It was great to be all together,” Orlando, Fla.-based Ryan, 44, told The Post during Allure’s seven-night cruise over spring break in March. “My in-laws live 2,000 miles from us, so it was quite the occasion.”

The eight-strong party was one of scores of multigenerational families marking birthdays, wedding anniversaries and other milestones on the world’s second-largest ocean liner, a title the 225,282-ton Allure shares with sister ship Oasis of the Seas, both launched in 2010. (The largest is Royal Caribbean’s Harmony of the Seas, at 227,000 tons.)

It’s a growing trend, according to Cruise Lines International Association (CLIA). The organization’s 2014 consumer study, the most recent it has available, found nearly one-fifth of all American cruise passengers vacation with extended family.

“They can explore amazing destinations, choose amenities and activities for each family member, all in a stress-free and fun travel environment,” says Cindy D’Aoust, CLIA’s president and CEO.

No surprise, then, that a little industry has sprung up around these group trips, pitching customized T-shirts and stationery. One online company, Zazzle, sells “Family Reunion Cruise Invitations” for $2.60 per card.

Certainly, the 18-deck Allure of the Seas is an ideal place to host such a shindig. With a capacity for a staggering 6,318 guests, the goliath is suitable for even the entire Duggar clan.

My family of four is humble by comparison — me, my husband and our two young kids — but we observed plenty of larger groups like the Barsons taking advantage of onboard facilities that appeal across age groups.

The most remarkable innovation on Allure is its “neighborhoods” concept — seven distinct, themed areas dotted around the floating hotel.

They include so-called Central Park, where the center of the ship opens to the skies to reveal lush, tropical grounds that span the length of a football field.

The park’s main piazza resembles a “town square” for al fresco dining at specialty restaurants; munch on upscale Italian from Giovanni’s Table while listening to strolling jazz musicians or brass bands.

Another outdoor zone called The Boardwalk, nostalgically inspired by Coney Island, attracts families with a colorful original carousel and spectacular Aquatheater. That 735-seat space is where we watched the jaw-dropping “OceanAria” show, featuring acrobats who high-dive from 60-foot platforms into a pool controlled by hydraulics.

Stretching the 1,187-foot length of the ship is the pool and sports zone, a playground for anyone from toddlers to seniors with four swimming pools, two surfing simulators, a nine-hole miniature golf course and the adults-only glass-paneled Solarium — an enormous space reserved for grown-ups that includes Jacuzzis, sun loungers and cocktails aplenty.

Also targeted at over 21s, there’s a “nightclub district” that includes intimate venues like the Prohibition-themed Jazz on 4, dance bars such as Dazzles, a live comedy club and the obligatory casino.

With its noisy, smoky atmosphere, that was the only part of the ship to which my 9-year-old daughter, Daisy, objected. More to her taste was the 775-seater Studio B, where she watched an ice-skating show, and the Amber Theater, where we played a particularly tense game of bingo in the vain hopes of winning our next cruise.

According to the CLIA survey, some 46 percent of cruise passengers bring along children — and Allure is sure to cater to them. Daisy threw herself into the Adventure Ocean program for kids aged between six months and 11. (Sadly, our son Bobby, 6, opted out.)

Equipped with a science lab, cinema and workshops, the club is free during the day, but charges $7 per child per hour for the so-called “late-night party zone” between 10 p.m. and 2 a.m. I’m ashamed to admit we once picked up Daisy at one in the morning!

We shared a slightly dubious slice of pizza along the Royal Promenade — packed with shops, cafes and bars — on the way back to our suite.

That slice, though, was the only average meal we had on the cruise. We dined using the cost-free so-called “My Time” option in the more casual Adagio dining area, which means we chose what time we ate. Others attended one of three buffets or picked a formal sitting in the main dining room at either 5:45 or 8 p.m. (all included) or booked one of the eight specialty restaurants (which cost extra).

Passengers of all ages like getting off the boat, too. On our cruise of the western Caribbean from Fort Lauderdale, Fla., our three ports of call were the tiny beach cove of Labadee on Haiti, jungly Falmouth, Jamaica, and the island of Cozumel, Mexico.

In dock, we ventured out together — though you have the somewhat easier option of leaving your kids in the children’s club on board — on excursions including a tubing trip down a Jamaican river and a make-your-own chocolate and piñata adventure on Cozumel.

The Barson/Fuller family also had bonding experiences on visits to Dunn’s River Falls in Jamaica and the Mayan ruins of the Coba pyramid in Mexico. That mixed-age crew found that even when given the option to hang out separately, they preferred to spend much of the time together.

“Our sons were free to do their own thing on the ship, yet enjoyed hanging around with us on the deck chairs,” dad Ryan says. “The excursions were extra fun because their grandparents came along.”

Encouraged, I’m dreaming of my own big family reunion on another cruise, bringing in my parents and sister from England and in-laws who live on the West Coast. If only we’d won that bingo game!

Prices for Allure cruises vary depending on the season and what promotions are on offer. In September, under a current deal, a family of four can embark on a seven-night Caribbean itinerary like ours with rates starting at $665.03 per person for a large interior stateroom. Regular rates, though, go from $915 per person for the same stateroom.