President Reagan, vowing no retreat from his pledge to "rearm America," is proposing a huge, 20 percent increase in defense-related expenditures next year that will boost actual outlays to $221 billion and raise the overall amount that can be spent or committed to $263 billion.

The Reagan administration's new budget relies on a heavy dose of warnings about the Soviet military threat and confidence that a popular consensus remains for a military buildup in order to propose a record peacetime hike of $43.7 billion in Pentagon budgetary authority next year, including a $33.1 billion boost in actual spending.

The increase for defense, the president said, "is the largest discretionary increase proposed in the budget," meaning that his administration had made a very clear decision not to back away from attacks in Congress on Reagan's priorities. "A year ago," Reagan says in his budget message, "every component of military strength was flashing warning of neglect, under-investment and deteriorating capability. Today," he claimed, "health is being restored."

That health will be expensive. The Pentagon's share of the entire federal budget in fiscal 1983 will be 29.2 percent, up 5 percentage points from 1981. By 1987, under Reagan's $1.6 trillion five-year defense plan, that percentage will rise to 37.2 percent.

For the fiscal year beginning next Oct. 1, the White House is asking Congress for $258 billion in new Pentagon spending authority, that is the ability to spend and also commit money on long-term contracts. That is a 20 percent growth over this year's $214.2 billion measured in current prices but a 13.2 percent increase when inflation is taken into account.

Actual spending is due to increase from $182.8 billion this year to $215.9 billion in 1983, an 18 percent increase in current prices but 10.5 percent in "real" terms after inflation.

The total of $263 billion for defense is reached by including more than $5 billion in nuclear weapons production in the Energy Department budget. This fiscal year's total is $219 billion.

In addition, there will be a $2.3 billion defense supplemental appropriation request sent to Congress primarily to cover higher-than-expected inflation costs in the current fiscal 1982 budget.

Deputy Secretary of Defense Frank C. Carlucci, in briefing reporters yesterday on the new defense budget, argued that one reason the new budget is big is because it is a "reform" budget in which the Pentagon tried to get away from past problems of "hidden costs and under-pricing" by using more realistic cost and inflation figures. Similarly, he said the new budget includes a sharp increase in mass buying of ships and planes so as to achieve economies over slower production and also to get equipment into service faster.

For example, the new budget includes an unprecedented request for $6.8 billion dollars in one year to complete two new nuclear-powered aircraft carriers, the sixth and seventh in the U.S. fleet. Carlucci claimed that by merging these two efforts, some $750 million can be saved in labor and inflationary costs while the Navy will get these ships in 1989 and 1991, two years ahead of schedule.

In general, the new defense budget includes big chunks of money for virtually all of the main military weapons projects that are already under way. Few, if any, projects have been cut.

On the other hand, there are few, if any, new projects as the Pentagon puts major emphasis on improving the combat readiness, training and sustainability of conventional forces, removing the backlog of maintenance that has built up in shipyards and aircraft repair depots, and modernizing the nation's nuclear-strike arsenal.

Many defense specialists believe this emphasis on readiness is the right thing to do, but it is also the easiest thing to cut if the Congress is seeking immediate reductions in spending to help get the federal deficit down. Cutting the big visible weapons projects such as the MX missile or B1 bomber produces relatively little immediate spending savings because the contracts span many years.

Here are the highlights of the budget:

* Strategic nuclear forces--$23.1 billion, an increase of $6.9 billion over this year, is requested. The new B1B bomber would get $4.8 billion to continue development and to buy the first seven planes. The 10-warhead MX missile more than doubles in cost to $4.5 billion next year, including further development and purchase of nine missiles.

Two more Trident submarines--the 10th and 11th of their class with each carrying 24 missiles--are budgeted for $3 billion. Production of Trident I missiles continues along with stepped-up development of the more accurate Trident II. As another quick fix to balance the alleged vulnerability of U.S. land-based missiles to Soviet attack, production will be stepped up on nuclear-tipped cruise missiles for ships and submarines.

Army research work on antimissile defense will also double to $754 million as the administration grapples with the still unsolved problem of protecting the MX missiles.

* Conventional forces--Accelerated procurement of 182 Air Force jet fighters and attack planes and 146 for the Navy and Marines are part of $106 billion for general purpose forces, a 20 percent increase over this year. Fuel stocks will be increased 7 percent, along with increases in ammunition, spare parts and war-reserve stocks.

The Army will get 600 new infantry fighting vehicles for $965 million and 776 M1 tanks for $2 billion. Several Army systems still under a technical cloud in Congress, such as the advanced attack helicopter, Patriot and Divad air defense systems, also get substantial funding. There is also $377 million for chemical warfare, mostly defensive equipment but also the beginnings of new weapons manufacturing.

The military will get an 8 percent pay raise, compared with 5 percent for civilian federal employes. Despite the intention to give the United States more military reach worldwide, there are no increases planned in the size of the Army and relatively small increases of 16,000 persons for the Navy, 19,000 for the Air Force and 3,000 for the Marines. There is a 54,000-person increase planned for the selected reserves, however.

* Naval forces--Aside from two carriers and two more Trident missile-subs, the $18.6 billion 1983 Navy shipbuilding program includes three new cruisers, two more nuclear-powered attack submarines and nine other vessels.

Although the president says the United States is seeking only safety and not superiority in the nuclear-missile balance of power with Moscow, the United States is seeking "maritime superiority." Thus, he outlined a $96 billion, five-year shipbuilding plan to provide that superiority which calls for building 133 ships, roughly double the plan of the previous administration, to increase the fleet to more than 600 vessels from about 450 today.

* Mobility forces--The emphasis on getting troops to the Persian Gulf or other troublespots continues with more than $11 billion allocated to fixing C5 transports, buying a new version of that plane and buying new KC10A tanker/cargo aircraft in addition to increased conversion and chartering of vessels to pre-position equipment overseas.

In an effort to dramatize what Carlucci said were also savings in the defense budget, the Pentagon claimed it would save more than $51 billion by 1987 through restraints on retired pay and civil service compensation in combinations with reductions on acquisitions and various department operations.

Carlucci told reporters yesterday "we are optimistic" about the budget's chances on Capitol Hill if it is weighed against the real threat of the Soviet Union rather than against social programs. He called it "a minimal budget" necesssary to maintain security and noted that "a lot of people were predicting doom and gloom last year but we got substantially what the president asked for" from Congress.