An article yesterday incorrectly reported the Pentagon's projected fiscal 1983 budget, which is roughly $215.9 billion. The accompanying chart on defense spending should have listed projected expenditures in the Houston and Cleveland areas as $.583 billion and $.535 billion, respectively. The net gain per family in the Dallas area should have been listed as $3,600.

The Washington region, home of the Pentagon and numerous military bases, is the nation's leading beneficiary of military spending and gets back more than two dollars for every tax dollar it contributes to the defense budget, according to a new study.

The region receives nearly $5.6 billion more in defense money than it contributes in defense taxes, for a net plus of about $6,200 per family, according to the study, which examines the impact of Pentagon spending on the economy.

The Baltimore region and the Norfolk and Newport News areas of Virginia also get back considerably more from military spending than they pay in taxes, the report said.

But for two-thirds of the metropolitan areas in the nation, including Richmond, increased military spending doesn't benefit the home economy and is, instead, a "tax burden" that costs American cities billions of dollars, the study said.

The biggest tax burdens for defense fall on the New York, Chicago, Detroit, Houston and Cleveland areas, according to the study, while the Washington, San Diego, St. Louis, Newport News and Dallas regions lead the nation in getting back more for their military dollars.

The study, "Bankrupting American Cities," was done by Employment Research Associates, a private Lansing, Mich., firm that specializes in defense spending and its economic impact. The study focused on the tax impact of the Pentagon's projected$214 million budget for fiscal 1983, surveying the net dollar losses or gains that such military spending is expected to have on the nation's 266 Standard Metropolitan Statistical Areas.

Increased military spending, according to the study, "means the federal government acts as a giant siphon funneling tax money out of 176 metropolitan areas into those which have large military bases or very high military contracts." The report concluded that "accelerated military spending will result in the impoverishment of major sections of American society and worsening budget problems for most metropolitan areas."

A Defense Department spokesman said yesterday that Pentagon officials have not yet seen the study and could not comment on it.

The projected dollar gain for the Washington region's military expenditures is consistent with the heavy concentration of defense activities in this area. Projected military spending here for fiscal 1983 is expected to be about $9.8 billion, or nearly $5.6 billion more than the $4.2 billion the region is taxed for defense.

The Baltimore region, according to the study, is taxed $2.2 billion a year for defense but can expect military expenditures of about $3.1 billion. This gives it a net dollar gain of nearly $1 billion, or roughly $1,500 per family. Norfolk, which is taxed $657 million and gets back $3.3 billion, has a net dollar gain of $2.6 billion, or about $11,400 per family. That net gain placed it sixth in the nation.

Newport News, in fourth place, will pay $312 million in defense taxes and get back $3.2 billion in military expenditures. This gives the region a net dollar gain of $2.9 billion, or $27,600 per family.

Marion Anderson, director of the research firm, cautioned, however, that the gains per family reflect the high concentration of military personnel in the two Virginia cities, which are major shipbuilding and military employment centers.

Richmond comes out on the minus side of its defense tax dollar returns, paying out about $687 million and getting back about$450 million. This amounts to a net loss of about $237 million, or roughly $1,300 per family.

The biggest loser, in terms of defense taxes paid compared to military spending in its area, is New York City, according to the study. New York will pay about $11.7 billion in taxes for defense and receive only $3 billion worth of military spending in the region. That amounts to a net loss of about $8.7 billion, or about $3,100 per family.