What started as an addition to display 1,100 artworks on loan from the Fisher family has ended up with more than 4,000 new works in the largest modern and contemporary art museum in America and the largest museum of any kind in Northern California, as measured by gallery space.

The San Francisco Museum of Modern Art announced Wednesday that it will reopen May 14, 2016, after being closed for three years of expansion. When it does, it will have seven floors of exhibition space, and one of those floors, the fourth, is larger than all five floors from the original building designed by Mario Botta that opened 20 years ago.

“This is a game changer for San Francisco,” said SFMOMA Director Neal Benezra. “It lifts us to the top ranks for museums of modern and contemporary art in the world.”

The stand-alone 10-story architectural statement by the international firm Snohetta rises over the original five-story brick box like a gray silo looming over a red barn. The new SFMOMA meets the old one at a seismic joint and flows as one to create 460,000 square feet. This includes 145,000 feet of interior gallery space, which is 20,000 feet more than at the Museum of Modern Art in New York City, the next largest. The Botta building had approximately 69,000 feet of exhibition space.

In the Bay Area, SFMOMA is now the largest art museum, surpassing the Oakland Museum of California at 110,000 feet. In the city, the de Young Museum is second at 84,000 square feet. Statewide, its exhibition space is 50 percent larger than the Getty Center in Los Angeles and is second only to the Los Angeles County Museum of Art, the Smithsonian of the West, which boasts 230,000 feet.

Thousands of new works

To fill the space, SFMOMA has recently acquired or been promised 3,000 works from 200 donors for its permanent collection. Six hundred of these will be introduced when the museum reopens, including works by Pablo Picasso, Jasper Johns, Ed Ruscha, Diane Arbus and Robert Rauschenberg.

And that’s not counting the 1,100 works on 100-year loan from the Doris and Donald Fisher Collection, which were the incentive for the new building in the first place. Some 260 of these, by 68 artists, will open the new museum. It will take four galleries just to show the Fisher holding of paintings by Ellsworth Kelly. Then there are the 24 works by Sol LeWitt, 23 by Gerhard Richter and 21 by Andy Warhol.

The project was privately financed at a cost of $305 million, compared with the $60 million it cost to build the original museum. The admission price to recoup that investment has not yet been set, but it will be free for anyone under age 18, not under 12 as it was before.

Free to anyone of any age will be the first two floors. The general public is welcome to walk through the old entryway on Third Street or the new one on Howard and mingle among a massive steel sculpture by Richard Serra, a suspended mobile by Alexander Calder and a mural by LeWitt.

“We’re hoping pretty much the whole city of San Francisco will stop by to check out the building. Then they will be so seduced by what they see that they will pop for a ticket,” said Deputy Museum Director Ruth Berson, who allowed The Chronicle in for a hard hat tour last week.

It was a long walk. The Snohetta building alone is 235,000 square feet, twice the size of the Broad, the new museum for contemporary art that opened in Los Angeles in September.

“The addition of the Fisher Collection and our own collection campaign are going to be transformative for anyone who comes to the Bay Area,” Benezra said. “When you put the two collections together, we are going to take our place among the handful of very fine museums of contemporary art and photography in the world.”

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And it wouldn’t have happened if Gap founders and art collectors Don and Doris Fisher had not lost a long battle to build their own free museum of modern art on the Main Parade Ground of the Presidio of San Francisco.

When it became clear that Don Fisher would not get the modern architectural statement he wanted in the Presidio, he offered his collection to SFMOMA, where he served on the Board of Trustees. The announcement that the Fisher collection would be coming to Third and Howard was made in September 2009, just days before Fisher died, at age 81.

What happened next happened fast compared with the Presidio quagmire. The international firm of Snohetta was chosen to design a sleek horizontal shape with an angular roof and distinctive wavy exterior clad in lightweight cement panels.

SFMOMA then paid to build the San Francisco Fire Department a new station on Folsom, so that it could demolish the old station on Howard. The new Snohetta building fronts on Howard and meets the old Botta building toward the rear, with the combined complex surrounding the W Hotel on the northeast corner of Third and Howard.

Partners in a dance

Combined, the two SFMOMA buildings serve “as dance partners,” said lead architect Craig Dykers of Snohetta. “The existing building is a wedding cake that steps up in layers, and our building continues those steps upward.”

Steps inward to the museum can be reached either from a new entrance on Howard or from the original on Third. The Third Street entrance opens onto the old atrium, which is now washed in daylight from the signature oculus. This is because the central staircase, with switchbacks rising four floors, has been removed and the light streaming in from above is no longer bisected by the stairs.

“With the attendance that we are planning to have, you couldn’t exit everybody from the building with that narrow staircase,” said Berson. “The upside is that we have a lot more daylight coming in through the oculus.”

The old granite stairway was not wide enough to meet current safety codes, so it has been replaced by a single flight of terrazzo stairs that are wider, leading to the second-floor entrance hall.

From there, the visitor passes two metal strips that run parallel along the width of the building. These mark the seismic joint where the old building meets the new one. Step over a 2-foot seam and you’ve gone from one building to another. Each has its own foundation and will move independently in the event of a major earthquake.

The seismic joint is also where people coming from Third Street will intersect with people coming up an exterior staircase and through the new Howard Street entrance.

“If SFMOMA has a Grand Central Station,” said Berson, “you’ve just stepped into where the info desk and the giant clock are.”

Grand Central here is called Schwab Hall, and it overlooks the Roberts Family Gallery on the ground floor. This is where Richard Serra’s “Sequence” sits.

Anybody can see it from street level, through a wall of windows, and anybody can come inside and take a seat on several rows of amphitheater-style benches.

The second-floor free zone is nearly 45,000 square feet with art everywhere. The second floor also has galleries that require paid admission, and art-wise the only way to know you’ve gone from the free zone to the ticketed zone is that the flooring advances from gray terrazzo to white maple.

All the old favorites from the permanent collection — Matisse’s “Semme Au Chapeau,” Mark Rothko’s “No. 14,’’ Jackson Pollock’s “Guardians of the Secret” — will be back on the second floor, where they were before the remodel.

Beyond the second floor

Everything above the second floor takes a ticket. Then, as now, the third floor is dedicated to photography, always a strength of the collection. But now the photography floor, renamed the Pritzker Center for Photography, is roomy enough to store the entire inventory of 17,800 images.

Also on the third floor will be a coffee bar, an indoor/outdoor gallery dedicated to the mobiles of Calder, and a sculpture terrace with a green wall that rises 28 feet and runs from Minna to Natoma street. Fifty thousand plants amount to “the largest living wall in the Bay Area,” said Berson.

Get through the first three floors and there are still four floors to go. You have not yet seen the bulk of the Fisher contribution, which Benezra calls “one of the truly great collections of contemporary art in the world.”

It is spread among floors four through six, and so are the views of the San Francisco skyline, available from window seats and a new seventh-floor terrace, the highest at the museum.

“You can no longer see the whole museum in one day,” Berson said. “But the good news is you can come multiple times and focus on something different.”

That’s one strategy for selling tickets. Meanwhile, SFMOMA’s status as the largest in the land probably won’t last. MOMA in New York has bought and leveled the neighboring American Folk Art Museum on West 53rd Street to add 40,000 square feet of gallery space.

Sam Whiting is a San Francisco Chronicle staff writer. E-mail: swhiting@sfchronicle.com Twitter:@samwhitingsf

Online extra

Video: Ruth Berson shows us around the new SFMOMA at http://bit.ly/1OTf8c8.