DURING THE FIRST presidential debate, President Obama charged that Mitt Romney had proposed “$2 trillion in additional military spending that the military hasn’t asked for.” Though Mr. Romney didn’t contest the statement, the truth is more complicated. Mr. Romney is proposing to fully fund the four-year plan laid out by the Defense Department, and Mr. Obama’s former defense secretary, Robert M. Gates, in 2010. Mr. Obama scrapped that scheme this year to cut $500 billion from the Pentagon over a decade.

Mr. Romney would restore that funding as well as an earlier round of cuts by Mr. Obama; he would also establish “a goal” of spending 4 percent of GDP annually on defense, compared to about 3.5 percent in Mr. Obama’s latest budget. A gradual increase to 4 percent over 10 years would yield the $2 trillion figure Mr. Obama cited. In historical context, that’s not a big number: During the Cold War, defense spending averaged more than 6 percent of GDP.

Administration officials argue that defense spending is better measured by needs than by an arbitrary percentage of the economy. True enough; but then, the United States has been pressing its NATO partners for years to commit to just such a GDP percentage. The point is to ensure that military preparedness is not sacrificed to fund more popular programs. By cutting defense while resisting serious reforms of Medicare and Social Security, Mr. Obama is doing just the opposite.

What would Mr. Romney’s added money buy? He says he would reverse the 100,000 cut in military personnel Mr. Obama is planning, which would take the Army and Marines back to where they were in 2001. He would increase Navy shipbuilding from nine to 15 vessels annually, and he would invest more in missile defense. James Jay Carafano, a defense expert at the conservative Heritage Foundation, calculates that by meeting the 4 percent target Mr. Romney could increase the Navy to the 346 ships recommended by a bipartisan, congressionally appointed panel that reviewed the Pentagon’s 2010 plan — compared to 263 ships under Mr. Obama’s budget.

Mr. Obama’s cuts in personnel rest on the dubious assumption that there will be no need to fight land wars in the coming decade; while no one wishes for such wars, trends in the Middle East make that a risky bet. The shrinking Navy, in turn, is at odds with Mr. Obama’s strategy of building up forces in Asia as a hedge against a belligerent China. In all, Mr. Romney’s plan would better respond to U.S. strategic needs, if a responsible way could be found to pay for it.

As both candidates have acknowledged, large savings could be made in the Pentagon’s civilian administration and contracting — not to speak of soaring salary and benefit costs, which take 30 percent of the defense budget. But Mr. Romney would have to find hundreds of billions of dollars to fund the 2010 Pentagon wish list, and much more for the 4 percent goal. Given his unwillingness to contemplate tax increases or other revenue measures, military spending is one more area where Mr. Romney’s math doesn’t add up.