As President Obama measures the potential burden of a new war strategy in Afghanistan, his administration is struggling to come up with even the most dispassionate of predictions: the actual price tag for the anticipated buildup of troops.

The calculations so far have produced a sweeping range. The Pentagon publicly estimates it will cost $500,000 a year for every additional service member sent to the war zone. Obama’s budget experts size it up at twice that much.

In coming up with such numbers, the White House and the military have different priorities as well as different methods.

The president’s advisors don’t want to underestimate the cost and then lose the public’s faith. The Pentagon worries about sticker shock as commanders push for an increase of as many as 40,000 troops.

Both sides emphasize that their figures are estimates and could change -- in fact, a Pentagon comptroller assessment this month put the number closer to that of Obama’s Office of Management and Budget.

Still, budgeting and politics are entwined, and numbers can always support more than one point of view.

The Bush White House minimized costs as it moved toward war. Obama is weighing skeptically an escalation of a war he didn’t launch. In his campaign, Obama promised not to tuck war costs away, off federal budget books.

“Our resources in manpower, our resources in human lives and our resources in money are not infinite,” White House Press Secretary Robert Gibbs said in an interview. “The notion that we wouldn’t take each of those things into account does not make a lot of sense to this commander in chief.”

All of those elements are under consideration as Obama wraps up a review of war strategy. He is expected any week now to respond to requests from his commander in the region for a strategy change and for additional forces. The White House could announce an increase of 20,000 to 40,000 troops shortly after Thanksgiving.

During a recent session of his war council -- where one contingent has questioned the wisdom of sending more troops -- Obama asked how much it would cost to pay for the troops Gen. Stanley A. McChrystal has requested. The president sought an exact accounting, a request that turned out to be more complicated than anticipated.

The Office of Management and Budget says adding 40,000 troops would cost about $40 billion a year, or $1 million each. White House officials included in their estimate everything they consider necessary to wage war, including troop housing and equipment.

Inside and outside the Pentagon, some suspect an effort to undermine support for a troop increase. “The large-scale message has been, ‘This is going to be hard and expensive,’ ” said Thomas Donnelly, an American Enterprise Institute fellow and defense expert.

The Pentagon arrived at its much lower estimate by dividing its war funding request by the number of troops throughout the region: 68,000 in Afghanistan and up to 95,000 in supporting roles elsewhere, such as on nearby ships or in surrounding countries.

The Pentagon cost includes higher combat wages, extra aircraft hours and other operations and maintenance costs, but omits such items as new weapons purchases -- one-time costs that vary by year -- and support equipment like spy satellites and anti-roadside-bomb technology.

The Pentagon also does not try to estimate costs of new bases for additional soldiers.

But in a memo early this month, obtained by The Times’ Washington bureau, the Pentagon’s own comptroller produced an estimate that broke with the customary Defense formula and did include construction and equipment.

That memo said the yearly cost of a 40,000-troop increase would be $30 billion to $35 billion -- at least $750,000 a person. An increase of 20,000 would cost $20 billion to $25 billion annually, it said -- a per-soldier cost equal to or greater than the White House estimate.

Even determining past spending is a fuzzy endeavor: Big chunks are paid through emergency measures and are not calculated into the total.

Under questioning by the House Armed Services Committee this month, a Congressional Budget Office expert couldn’t say how much it costs to run the wars in Iraq and Afghanistan.

“I find it astonishing that, eight years into this, we haven’t nailed it down with precision,” another witness at the table, David Berteau, director of the Defense Industrial Initiatives Group of the Center for Strategic and International Studies, said later.

And yet the effort is necessary, said Stephen Daggett of the Congressional Research Service: “If the budget is going to be constrained, one of the questions we have to ask is whether we can sustain the increases in forces.”

Partisans of all stripes are likely to think first about intangibles, including American tolerance for troop casualties and support for sending new troops to Afghanistan.

Democratic leaders say money won’t determine their level of commitment.

“You have to look at the mission first,” said House Armed Services Committee Chairman Ike Skelton (D-Mo.). “You absolutely start with that.”

Obama’s decision will not be based on money, his press secretary said.

“The president is going to pick the strategy that’s most in our national security interest,” Gibbs said.

“Along the way, the health of our forces, the toll on lives and the financial costs will all be discussed.”

cparsons@latimes.com

julian.barnes@latimes.com