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A change in the state’s testing program meant to close an $8 million budget gap could have far-reaching consequences for city students and schools, principals say.

The Board of Regents voted yesterday to do away with the January administration of the state exams required for high school graduation. The tests will still be given in June and August.

City school officials criticized the change, which had principals across the city lighting up their colleagues’ e-mail inboxes with protests of the change. “The state shares our belief in high standards that prepare students for college — so it is somewhat disheartening that the Regents would make a decision that undermines the hopes of high school students who take courses and exams to graduate mid-year,” said Chancellor Dennis Walcott in a statement.

In 2010, about 360 students used January exams to graduate midyear, out of about 3,800 total midyear graduates, according to Matthew Mittenthal, a Department of Education spokesman. Under the new system, those students would have had to wait until June to try to graduate.

But principals say those figures underestimate the effects of the change. Many students use the January dates to increase the number of times they take the Regents exams, which in turns increases their chances of passing in the long term. Students also use the January administration to spread out their tests and avoid burnout.

“Regents exams — how you schedule them and how you prepare for them is very strategic,” said Musa Shama, principal of Francis Lewis High School. “This is one of the things that changes the game right now. … I think this will have a tremendous impact on all high schools. I certainly think that high school graduation rates will take a hit as well as Regents pass rates, which would also affect progress report grades.”

At Francis Lewis, students typically take the U.S. History Regents exam in January of their senior year. Students who fail have another chance in June to pass the exam, which the state requires for graduation. Given two shots to pass, most students do. But with just a single chance, at least some students are likely to see their graduations delayed, Shama said.

The effects could be damaging both for students and for their school leaders, who face consequences if their performance slips, he said.

“Even if it’s only 10 percent, that’s a lot of kids. And 10 percent on a graduation rate — that may change the conversation about a school,” Shama said. “If I took a 5 percent hit, we would be below 80 percent. I would start freaking out.”