Former students of for-profit colleges who took out federal loans defaulted on them twice as often as their peers from public institutions during a recent three-year period, the government reported Friday.

What is known as the three-year cohort default rate was 22.7 percent for for-profit schools, 11 percent for public schools and 7.5 percent for private, nonprofit schools. For all sectors combined, the rate was 13.4 percent.

The rate took into account defaults that occurred by Sept. 30, 2011, for borrowers who began repayment in the fiscal year that began Oct. 1, 2008.

The overall three-year rate, making its official debut this year, is down slightly from a trial version published last year — 13.8 percent. Schools with a default rate above 30 percent must take steps to prevent defaults. They risk losing eligibility for federal financial aid if the rate tops that level three years in a row.

For years, the default rate was measured in two-year cohorts. Congress recently extended the span to three years in an effort to capture a more complete picture of the default problem. The overall two-year rate this year is 9.1 percent.

Default rates are closely watched in higher education as more students borrow to pay for college. This week the Pew Research Center reported that 19 percent of the nation’s households owed student debt in 2010, more than double the share found two decades earlier.

“We continue to be concerned about default rates and want to ensure that all borrowers have the tools to manage their debt,” Education Secretary Arne Duncan said in a statement.

Steve Gunderson, president of the Association of Private Sector Colleges and Universities, an industry group, said in a statement that for-profit schools would redouble efforts to ensure students understand how to control their debt. But he said the government should also improve loan collection programs and give schools authority to limit loans to the direct cost of education. “We all must do more,” Gunderson said.

The Washington Post Co. provides higher education for profit through its Kaplan education unit. The three-year default rate for Kaplan University, the largest Kaplan school, was 25.9 percent. At a few Kaplan schools the rate topped 30 percent. For example, at Kaplan Career Institute in Boston, it was 33.6 percent.

Kaplan spokesman Mark Harrad said the default rate held steady or improved at most Kaplan schools. “Obviously we will work with any school that needs improvement,” he said.

Federal officials said 218 schools nationwide had default rates higher than 30 percent.