The Carter administration estimates it will take nearly $25 billion over the next five years, or nearly twice as much as the government is spending now, to finance currently planned expansion of U.S. nuclear weapons production.

For the first time, one official said yesterday, the administration "has priced out what the president has . . . ordered" in his annual nuclear stockpile report. That is the document the chief executive signs each year that by law sets production targets for the next three years and allows procurement of long-lead-time items over the coming five years.

The bulk of the new funds needed will be used to pay for increased production of nuclear weapons materials, such as plutonium and tritium.

The administration has determined that long-term nuclear weapons needs cannot be met by the current output of the three production reactors now in operation at Savannah River, S.C.

At present, the nuclear weapons complex is producing the new Trident I submarine-launched missile, the new Mark 12A warhead for the Minuteman III land-based ICBM, the B61 airdropped nuclear bomb, the Lance missile warhead, and the warhead for the new air-launched cruise missle. In final design stages and approved for production are another new strategic air-dropped bomb, a new ground-launched cruise missile, the Pershing II extended-range missile and a new eight-inch artillery shell.

Under design but not yet set for production are Mark 12A warheads adapted to the proposed new MX ICBM and another larger warhead for the same missile. In addition, designed but not approved for production are two controversial nuclear warheads for the Navy's Standard and Harpoon missiles. Still on the drawing board, but built into the long-term program, is the warhead for the Trident II missile.

All these weapons are to be built by a production complex that until two years ago was producing little more than one newly designed bomb a year.

A White House committee recently approved expanding production at the three existing Savannah River and initiating a "blending" operation that mixes supergrade plutonium with already produced lower grades in order to come out with a weapons grade.

To meet the costs of this increased production of special nuclear materials and the costs of additional workers at the seven facilities that make up the weapons production complex, Department of Energy officials are projecting the need for an additional $2 billion a year for the next five years, sources said.

For example, the planned DOE nuclear weapons budget for fiscal 1982, now being put together, will total about $5 billion, up from the $2.7 billion initially sought for fiscal 1981.

Another $1 billion, sources said, is being added to the DOE weapons budget over the next four to five years to pay for a long-delayed maintenance program for the seven plants around the country that make the parts and finally assemble the nuclear warheads. Several of these facilities, including the plant at Amarillo, Tex., where all the warheads are put together, do not meet the safety requirements of the government's own regulations.

In another move designed to facilitate funding of the nuclear weapons program, the Office of Management and Budget has agreed to give DOE two separate fiscal 1982 budget figures -- one for its civilian energy programs and the other for weapons programs. Under this procedure, any shortfall in the DOE defense side will not have to be made up at the expense of a civilian energy program.