WASHINGTON — One in every 20 federal prisoners could be eligible for early release under a potential sentencing change to be voted on Thursday for inmates convicted of crack cocaine offenses.

Congress passed a law last year substantially lowering recommended sentences for people convicted of crack cocaine crimes, ranging from possession to trafficking. The idea was to fix a longstanding disparity in punishments for crack and powder cocaine crimes, but the new, lower recommended sentences for crack offenders didn’t automatically apply to people already in prison. Now the six-member U.S. Sentencing Commission must decide whether offenders locked up for crack offenses before the new law took effect should benefit and get out earlier.

Up to 12,000 of the roughly 200,000 people incarcerated in federal prisons nationwide could be affected. A report by the commission estimates that the average sentence reduction would be approximately three years, though a judge would still have to approve any reduction.

“There is a tremendous amount of hope out there,” said Mary Price, vice president of Families Against Mandatory Minimums, an advocacy group for prisoners and their relatives.

“There is a potential that people could see their sentences reduced, for some quite dramatically.”