A bill passed by Congress Saturday will cut federal college aid to hundreds of thousands of students, though Harvard undergraduates are likely to be unaffected by the change.

The legislation permits the Department of Education to use a revised formula to calculate student eligibility for federal aid. Last year, the government tried to move to this formula, which could reduce awards to over a million students, but was blocked by Congress.

“It’s unfortunate, but it’s one of the things that happen when there isn’t enough money to go around,” said Brian K. Fitzgerald, director of Advisory Committee on Student Financial Assistance, an independent group set up by Congress to advise legislators.

According to Fitzgerald, families with incomes between $30,000 and $45,000 will be hardest hit, and 84,000 students will be entirely knocked off the federal grant rolls. The American Council on Education estimated that 1.2 million students would see reduced aid. Families with incomes of under $25,000 will not be affected, Fitzgerald said.

Harvard students, however, will most likely be unaffected because Harvard’s need-based financial program will make up for any reductions in government aid.

“We would continue to meet the full need of all our students,” said Sally C. Donahue, director of financial aid for the Faculty of Arts and Sciences.

“On the national level, it would present a difficult situation for schools that don’t have the funding we have,” she said.

According to Sen. Jon Corzine, D-N.J., the changes will reduce the amount of federal Pell Grants given to college students by $270 million.

“The Congress just threw students who need Pell Grants to afford a college education out into the cold,” said Corzine in a statement. Last year, Corzine wrote an amendment to an appropriations bill that suspended the formula from being used. Democrats attempted to add the same amendment to this year’s bill.

Almost 200,000 students a year currently choose not to go to college because of financial reasons, according to Luke Swarthout of the State PIRG for Higher Education, a group that advocates for more student aid.

“In somebody else’s calculus, the few hundred dollars [cut per person in financial aid] may be huge,” Swarthout said.

“It’s a very sad thing that Congress, behind closed doors, chose to take money out of students’ pockets at a time when educational costs are increasing,” Swarthout said.

Donahue said that Pell Grant funding has not increased in the course of the past 10 years, and has not kept up with the increase in educational need.

She said officials disappointed by the cut in federal aid are looking forward to next year’s reauthorization of the Higher Education Act, which will entail a thorough review of all guidelines governing the federal analysis of student need.

“The reauthorization will involve conversations that are much more in depth about the federal financial aid program,” Donahue said.