NEW YORK — Looking out over the quadrangle before him as students dashed from one class to the next, Dr. James Muyskens was feeling proud one recent afternoon, and why not? The college he has led for the past 11 years had just been awarded second place in a new ranking — ahead of flagship state schools, ahead of elite liberal arts colleges, even ahead of all eight Ivy League universities.

The college is Queens College, a part of the City University of New York with an annual tuition of $5,730 and a view of the Long Island Expressway.

Catering to working-class students, more than half of whom were born in other countries, Queens does not typically find itself at the top of national rankings. Then again, this was not a typical ranking. It was a list of colleges that offer the “best bang for the buck.”

“Elation,” said Muyskens, recalling his surprise when he learned of the honor. “Thrilled!”

Purists might regard such bottom-line calculations as an insult to the intellectual, social and civic value of education. But dollars-and-cents tabulations like that one (which was compiled by Washington Monthly), are the fastest growing sector of the college rankings industry, with ever more analyses vying for the attention of financially anxious high school students and their parents.

President Barack Obama sharply upped the ante this past August, with a plan not just to rate colleges on their value and affordability, but to tie those ratings to the $150 billion in financial aid that the federal government supplies each year. Should that plan come to pass, value would not just be a selling point for colleges, it would be a matter of life and death.

But not only is there no agreement on how to measure the value of a college, there is no agreement, or anything even close, on what value is in the first place.

“It’s a quest for the holy grail,” said Judith Scott-Clayton, a professor of economics and education at Columbia University’s Teachers College. “It sounds good, it sounds like something we’d love to know — to be able to rank the value of these institutions. But when it comes down to practicalities, it’s very, very difficult.”

U.S. News and World Report, whose annual suite of academic rankings have long been derided — and obsessively followed — by college presidents, now publishes “best value” lists as well. Princeton Review, which has advised decades of prospective students on the best party schools, 10 years ago began listing the best value schools, too. Forbes Magazine got in the is-it-worth-the-money game a few years ago, as did, among others, The Wall Street Journal, The Alumni Factor, Kiplinger’s Personal Finance and Payscale, a company that gathers data about the job market.

Some of these analyses approach value as largely a function of cost (How much is tuition? What subsidies do low-income students get?). Others define it as return on investment (How much do graduates earn?). Some factor in student satisfaction or academic ranking or graduation rates or economic diversity, all in varying quantities.

These widely divergent definitions produce wildly divergent results.

Queens College did splendidly in a list that emphasizes social mobility and civic virtue. (Another New York City public college, Baruch, took third place; No. 1 was Amherst.)

But on a ranking that emphasizes alumni salaries, like Payscale’s list of Colleges Worth Your Investment, Queens comes in 341st. The top spot there goes to Harvey Mudd College, in Claremont, Calif., which has a much higher tuition but whose graduates disproportionately enter the lucrative field of engineering. The top tier of U.S. News’ list somehow features Harvard, Princeton, Williams — and Soka University of America, a tiny Buddhist college in Southern California that admitted its first undergraduates in 2001.

The top five schools on Forbes’ most recent list are all national service academies, which charge no tuition. And a list by the Education Trust, an advocacy group, of all the colleges that do right by low-income students has only five entries, including Queens.

As for the federal government, no one yet knows how it will perform its evaluation. Arne Duncan, the education secretary, has said his goal is a ratings system, not a single first-place-to-last-place ranking, and that the ratings will compare only schools that are similar in their mission, their student population and so on. Harvard and Yale, that is; not Harvard and Soka University of America.

But Carolyn Hoxby, a Stanford professor and an author of an influential study about the failures of college as an engine for social mobility, said the effort is doomed to fail.

“I do not believe the federal government currently has the capacity to generate a ratings system that will even be neutral,” she said. “I think it’s more likely that it will be harmful to students.”

The rankings approach is working just fine for Queens College, which will prominently feature the Washington Monthly list in its new recruitment materials, but even its president has his misgivings.

“I happen also to be a philosopher,” he said, “and I know that if we go too far on the value added and cost, we’re going to have people too focused on the practical to explore.”

As he spoke, students in the next room were participating in a study group about the Middle East, learning how to engage with opponents without getting bogged down in accusation and retribution. Face-to-face interactions like that can be the most enriching part of college, Muyskens said, but they never make it into any algorithm of value.

He is proud of the school’s high score, he said, but added, “if it isn’t balanced by other perspectives, it’s dangerous.”