President Carter is leaving President-elect Ronald Reagan a record peacetime military budget of $196.4 billion for the coming fiscal year,

That total is the amount the president intends to request from Congress, not spend, and compares with $171.4 billion for the current fiscal year, an increase of $25 billion. The $171.4 billion for fiscal 1981 includes Carter's imminent request for $6.2 billion in supplemental funds and $5.1 billion for military construction.

Without allowing for inflation, the new total for fiscal 1982 -- the budget year starting Oct. 1, 1981 -- represents a 14.6 percent increase over fiscal 1981. But inflation will melt this increase down to around 4.6 percent, the so-called "real" increase.

Reagan will be pressured by conservatives in Congress and elsewhere to outdo this last Carter defense total, further jeopardizing the president-elect's stated intent to trim the federal budget and improve the national economy.

To keep his economic game plan from being shredded, Reagan would have to offset, at least in part, any big increases in defense spending with cuts in domestic programs, including ones popular with conservatives.

Although increasing the defense budget one percentage point to placate conservatives may not sound like much, a 1 percent increase in a $200 billion defense budget would cost $2 billion, or more than enough to run the District of Columbia for an entire year. (District Mayor Marion Barry is seeking $1.5 billion for fiscal 1982.)

Yet that same $2 billion would not buy much in the way of super-weapons. One Nimiz nuclear aircraft carrier, without its planes, costs more than $2 billion, and a single Trident submarine armed with missiles is running just about $2 billion.

Carter's final defense budget provides money for the new MX land missile, cruise missiles to be launched from bombers, more Navy warships, Army XM1 tanks. Marine equipment prepositioned in the Indian Ocean theater, and research on laser zap guns for space warfare. But more than half the nearly $200 billion is earmarked for the care and feeding of soldiers and other personnel costs. Another big slice is devoted to making the military better prepared to fight by buying the spare parts needed to keep planes flying and ships sailing.

Reagan, by his own pledges and those in the Republican platform he endorsed, is obliged to do more than that. His party's platform called for a new bomber, an air defense system, a permanent fleet in the Indian Ocean, faster production of aircraft and a 600-ship Navy, among other things.

Pentagon executives, in exit interviews, said they hoped Reagan would not feel bound by campaign rhetoric. Otherwise, they contended, the new administration would be spending more and getting less in terms of real national security.

"They should set aside the campaign rhetoric, ours and theirs," advised Defense Secretary Harold Brown. "They should look at our program. They should look at alternative programs, and make their own decisions."

Undersecretary of Defense William J. Perry, who has run the Pentagon's research and procurement for four years, said there is no way the new team could start on several big strategic programs at once, such as the MX missile and a new bomber, without taking money away from military readiness accounts. Bills already piling up for such weapons as the MX missile, Trident submarine and XM1 tank will force the Reagan team to space their new starts in weaponry, administration officials predicted.

Thomas B. Ross, the Pentagon's chief spokesman for the past four years, said "our basic mistake was not being forthright early enough on the need for higher defense spending.Candor goes a long way.

"In the first year we should have said that we have a better view from the inside; that in view of the Soviet buildup we are increasing the defense budget." Instead, Ross acknowledged, administration officials felt compelled to prove this June 10, 1976, statement by candidate Jimmy Carter to the Democratic Platform Committee: "Without endangering the defense of our nation or our commitments to our allies, we can reduce present defense expenditures by about $5 billion to $7 billion annually."

Ross cautioned the new team at the Pentagon against getting hung up the same way on campaign rhetoric. "I hope they'll say things look a lot better from the inside, and huge increases are not required. I think we made a mistake, and they can learn from that mistake. The government is like the press. You never like to admit you changed."

Reagan's designated secretary of defense, Caspar W. Weinberger, has called for reason in deciding how much is enough for the national defense. At a "town meeting" sponsored by the American Enterprise Institute on Oct. 17, 1972, Weinberger said:

"What is our foreign policy? What defense expenditures does it require? Initially, that is the order in which the questions must be addressed . . . . The identification of a threat to security does not automatically require an expenditure in the defense budget to neutralize it. The nation's total resources being limited, it is necessary to consider what is being given up to meet the threat. Some may feel it more important to invest money in education or health than to provide against what they consider remote contingencies in the national security field. The defense budget, in short, must be seen not only in terms of what we must defend ourselves against, but what we have to defend. The more we take from the commonwealth for defense, the smaller it becomes."

Weinberger has stressed in statements since then that the United States must spend more on defense, given the continued Soviet buildup. The question Carter poses to Reagan in the final defense budget, then, is not whether more is needed, but how much more. Reagan has said that the Soviets may be willing to slow down the arms race if the United States demonstrates, by higher defense spending, a determination to win it.

If the new president were to accept the recommendations of some conservatives and increase defense budgets by 7 percent a year, after allowing for inflation, and if inflation stayed at 10 percent annually, a fiscal 1982 budget of $200 billion would be pushed up to $376 billion by fiscal 1986. The five-year total would come to $1.4 trillion.