Zillow's analysis said Bay Area residents can expect to pay a whopping 44 percent of their income on rent or 39 percent of their income on their monthly mortgage payment.
"For-sale affordability is starting to look not so great, and for-rent affordability -- it's by far the worst it's ever been in San Francisco," Gudell said. "It kind of makes me wonder where that leaves people. Those are your two choices in terms of living, if you ignore your parents' basement for a moment."
She added, "San Francisco is an extremely unique case."
Zillow looked at the 35 largest metro areas in the United States. The most affordable places are areas like Detroit, where the population is growing slowly, or regions such as Chicago, where housing construction is keeping pace with growth and 906 permits were issued per 1,000 new residents.
Pittsburgh was at the other end of the spectrum from L.A. and the Bay Area -- 42,258 permits were issued per 1,000 new residents, despite the fact that people aren't exactly flocking there.
Cities like San Francisco and San Diego are drawing people partly because of tech jobs and intrinsic appeal. But regions with warmer climates, such as Las Vegas, Phoenix and Miami, are growing, too, Gudell said, and are especially attractive to foreign investors, snowbirds and retirees.
"In San Francisco you have a great job market, and it's booming," Gudell said. "So you're attracting a lot of new people. But you have growing pains because you're not able to keep up on the housing side of things. That's a real challenge right now."
The permit data pertain to housing units, Gudell said. So, a 50-unit apartment building, for example, would count as 50 permits.
The Bay Area was tops in the country, at $715,800, in Zillow's February calculations for its home value index -- the median of estimates of what homes are worth. In this category, Los Angeles ranked second, coming in at $533,700. Detroit, at the other extreme, was $114,400. And the U.S. median was $178,700.
Meanwhile, Zumper, a website that lists and analyzes rentals, has just released its national rent report for March, which found that San Francisco is still the most expensive city in the United States -- although rents dropped by 1.7 percent to a median of $3,400.
Oakland is now No. 4 in the country, with a median rent of $2,000. It's tied with Washington, D.C., and trails New York and Boston.