But it also generates their expected family contribution, or E.F.C. — a number that can easily be misleading. It’s often higher than many households can afford, and yet in many cases, like the Phipps family’s, it’s still not enough.

“For a long time, there has been this growing chasm between the need-analysis formula and accurately reflecting a student and their family’s ability to pay for college,” said Justin Draeger, president of the National Association of Student Financial Aid Administrators, which has members at nearly 3,000 schools.

The gap has grown wider not just because of the exponential rise in college prices, but also because of the E.F.C. formula itself. The formula, which stretches across 36 pages, often assumes families have far more income available to pay for college than they actually do, financial aid experts said, particularly in high-cost areas. The reason lies in its basic assumptions: that a family of four, for example, can subsist on less than $30,000, no matter where they live.



“Students have a lot more need than we are recognizing,” said Eddy Conroy, an assistant director at the Hope Center for Community, College and Justice at Temple University. “But the system isn’t really capturing that properly.”

Colleges use the E.F.C. to determine a student’s financial need — the difference between the college’s cost of attendance and the family’s expected contribution. Then, schools come up with a financial aid package. (About 400 schools and programs, mostly private colleges, also use another formula, known as the CSS Profile, to determine institutional aid, according to the College Board, which created the calculation.)

But unless a student attends a college that promises to meet 100 percent of his or her need — and the vast majority do not — students and their families will probably pay more than what the FAFSA estimates.