WASHINGTON — A bookkeeping change at the Education Department will kick hundreds of rural school districts out of a federal program that for nearly two decades has funneled funding to some of the most geographically isolated and cash-strapped schools in the United States.

More than 800 schools stand to lose thousands of dollars from the Rural and Low-Income School Program because the department has abruptly changed how districts are to report how many of their students live in poverty. The change, quietly announced in letters to state education leaders, comes after the Education Department said a review of the program revealed that districts had “erroneously” received funding because they had not met eligibility requirements outlined in the federal education law since 2002.

The department said it was simply following the law, which requires that in order to get funding, districts must use data from the Census Bureau’s Small Area Income and Poverty Estimates to determine whether 20 percent of their area’s school-age children live below the poverty line.

For about 17 years though, the department has allowed schools to use the percentage of students who qualify for federally subsidized free and reduced-price meals, a common proxy for school poverty rates, because census data can miss residents in rural areas.