Colleges typically want, in addition to a share of parents’ incomes, about 5 percent of the value of their assets, plus 20 to 25 percent of the students’ (Penn settles for just 5 percent of student assets). But there are differences in how colleges define assets. Cornell, Stanford, Columbia and Duke, for example, take into account home equity. Harvard and Princeton do not, and neither does the federal formula. New Yorkers might fare better with one of the elite private colleges, nearly all of which consider regional variations in cost of living. High medical expenses and kids in prep school? A few top schools, like Princeton, discount for both. The federal government and state colleges do not.

Joe Bagnoli has seen price shock from both sides — as a parent and now as dean of admission and financial aid at Grinnell College in Iowa. When his oldest child received aid letters from colleges, he said, “My reaction was: I just don’t have this kind of money.” This year, with two children in college, he borrowed $19,000 to come up with the parental contributions. He said some parents have trouble accepting the sacrifice involved in paying for college but stressed the immense long-term benefits.

“I have to think about whether the portion of the cost that’s assigned to me is commensurate with the return on investment,” he said.

This year, Grinnell changed its methodology, adding College Board variables to the federal formula. The new approach gives a more complete and fairer picture, he said, with some families judged to have much more need, others much less. Schools share the concern about divergent calculations and definitions, he said, and a group of need-blind colleges, called the 568 Presidents’ Group (after Section 568 of the Improving America’s Schools Act), compare notes and try to minimize differences.

But even within the group, colleges want the freedom to go their own way.

Precise comparisons among colleges are impossible, but the government’s vast database and net-price calculators provide a rough idea. Even within the rarefied group of highly competitive elites — with similar tuition and a vow to meet a student’s full financial need — what families pay varies widely. The database shows, for example, that for freshmen starting college in 2011, families earning $48,000 or less paid, on average, less than $5,000 a year at Harvard, Duke, the California Institute of Technology and the Massachusetts Institute of Technology, but more than three times that much at Boston College, the University of Southern California and Washington and Lee. For families in the $75,000 to $110,000 income bracket, Harvard families averaged less than $12,000; Northwestern, Oberlin and Tufts wanted more than twice as much.

The wealthiest colleges, of course, are the most generous across the board; Princeton, Harvard, Yale, Columbia and Stanford give need-based aid to families making more than $200,000.

None of this is obvious to the people who need the information most, like Will Damman and Abeer Syedah, freshmen at the University of Minnesota, Twin Cities. Both say they were intimidated by the high sticker prices of private colleges, but now wonder if they might have been able to shop around for a better deal.