The feds sued the city yesterday for allegedly shortchanging a retired detective on his pension by failing to consider the overtime he lost while serving as an Army reservist.

The suit seeks a recalculation of pension benefits for ex-Detective David Goodman and other cops who have performed military service, along with an award of the cash they were wrongfully denied.

The Manhattan federal court filing charges violations of the Uniformed Services Employment and Re-employment Act of 1994.

Goodman, a second lieutenant in the Army Reserves, served four tours of duty between 2002 and 2009 in Iraq, Afghanistan and Jordan.

“During the periods of Goodman’s active military service, NYPD employees had the opportunity to work, and did work, overtime hours,” the suit says.

“Had Goodman not been performing active military service, he would have been working overtime hours for the NYPD.”