The astronomical rise in Bay Area rents shows no signs of abating.

San Francisco landlords wanted a record average rent of $3,458 in the first quarter, up 1.9 percent from the fourth quarter and 13.2 percent from the first quarter of last year, according to a report from Real Answers. The report includes properties ranging from studios to three-bedroom townhomes in complexes with 50 units or more.

“Oftentimes lately, because the market is so hot, a lot of units don’t even hit the market” before they get rented out, said Samantha Chandler Duvall, a vice president with Chandler Properties, which manages about 5,000 units in San Francisco.

One of her leasing agents will be showing an apartment to six or seven prospective tenants and tells them about another that will be opening up soon. One of the prospects often snaps up the unit before her firm even advertises it or holds an open house, she said.

In the five-county San Francisco metro area, rents also soared. The average asking rent hit $2,370, up 3.3 percent from the fourth quarter and an astounding 14.3 percent higher than the first quarter of last year. These numbers include San Francisco, San Mateo, Marin, Contra Costa and Alameda counties.

The same thing is happening with homes for sale; they get sold without ever hitting the Multiple Listing Service.

In the nine-county Bay Area, year-over-year rent increases ranged from 11 percent in Napa County to 14.6 percent in Alameda County, the report said. Alameda rents are soaring as people who get priced out of San Francisco cross the Bay Bridge, said Nick Grotjahn, a spokesman for Real Answers.

Solano was the most affordable Bay Area county; rents there averaged $1,355 in the first quarter, up 12.7 percent year over year.

In Santa Clara County, rents were up 11.6 percent year over year — even though four new complexes with a total of 745 units were added to the survey since January 2014.

“Are we going to build our way out of this? In the near future, it doesn’t look like that’s going to be the case,” Grotjahn said.

San Francisco has an estimated 50,600 housing units in all stages of development, but they include properties for rent and purchase, including affordable housing. Only 6,700 were under construction in the third quarter, according to the City Planning Department’s latest pipeline report.

There are about 381,000 housing units in San Francisco, per 2013 U.S. Census data.

“I think the pipeline of developments coming into the market is only going to mute demand, maybe slow it down a little bit,” Grotjahn said. The only thing that could stop the increase would be a slowdown in job creation or “maybe it hits a saturation point, where people say, 'I can’t live here anymore, I’m going to commute.’”

The highest rents in San Francisco are generally in new buildings in the South of Market area, but they also have modern amenities such as dog runs, gyms, bicycle storage and concierges, Duvall said. Neighborhoods that provide easy access to the freeways and Caltrain, for people commuting to Silicon Valley, are among the hottest.

Duvall said that renters today “are a lot more organized than they used to be. They usually come with a folder, all their paperwork in order. New recruits will have a job letter.”

Her firm continues to get “really amazing” letters from prospective tenants. “They say, 'I love long walks on the beach, I love puppies, I’m a really nice guy.’ I say, 'You should put this on Tinder.’”