They rake in millions of dollars in federal tuition aid and still charge students more than $20,000 a year, on top of scholarships and grants.

Despite their high prices and promises of good jobs, more than a dozen of the Bay Area’s most expensive trade schools graduate fewer than half of their students, report alarming rates of students defaulting on their loans — or both.

While Californians have been hearing for years about runaway tuition at the state’s public universities, the state — and now the federal government — is demanding better results from a different sector of the higher education world: for-profit colleges.

Squeezing the for-profit sector would be “all to the good,” said UC Berkeley education Professor Emeritus Norton Grubb. “They enroll low-income students, they charge them high tuition, they get them all on student aid and then the students drop out, leaving them with no increased earnings potential and a lot of student debt.”

Take the $25,700-per-year Everest College in Hayward, where one in three former students did not earn enough to repay their student loans. Or the 1,900-student University of Phoenix in San Jose, which brought in $17 million in federal student aid in 2010-11; it reported a graduation rate of just 19 percent and a student loan default rate of 26 percent.

New federal regulations proposed for vocational programs and President Barack Obama’s initiative to tie student aid dollars — both grants and loans — to schools’ affordability and performance could also affect institutions like the $24,000-per-year Ex’pression College for Digital Arts in Emeryville, whose students relied on $9.7 million in federal education aid in 2010-11.

To understand where federal student aid money goes and how well the investment is paying off for students and taxpayers, this newspaper analyzed U.S. Department of Education data for more than 100 Bay Area schools. The analysis of federal financial-aid data from 2010 to 2011 found:

Nearly 30 percent of the $1.3 billion in federal Pell grants and student loans that flowed to Bay Area colleges went to for-profit trade schools.

Former students at for-profit schools accounted for nearly half of all federal loan defaults here, in the most recent count, though they make up just about 10 percent of the area’s college students. Loan defaults, which have serious credit score consequences, tend to occur when someone earns too little to pay off college debt.