A grateful President-elect Ronald Reagan, elated and suprised by the magnitude of his victory, tonight promised that he would work with President Carter to heal and unify the nation.

Praising his defeated rival, who early in the evening called Reagan to congratulate him as the Republican nominee was getting out of the shower at his Pacific Palisades home. Reagan said: "He graciously offered me his cooperation and I accepted it. We both want a smooth transition."

Later, Reagan descended to the ballroom of the Century Plaza Hotel here with his wife, Nancy, and thanked his supporters.

"I consider the trust you have placed in me sacred and I give you my oath that I will do my utmost to justify your faith," Reagan said.

After a campaign that had been bitter on both sides, a mood of generosity prevailed at the victory celebration in Reagan's well-appointed 19th floor suite. Both Reagan and his aides lauded Carter for his ready concession of defeat. Afterward, via national television, Reagan spoke with former president Gerald R. Ford, who had campaigned strenuously for him in the final weeks of the campaign. Without being specific, Reagan said he would find a role in his administration for Ford.

"I think that a former president always has a role, and any president that would ignore and not seek advice and counsel of a former president would be wasting a great asset, and I'm not going to waste a great asset," Reagan said.

Earlier, when the first heavy Reagan returns started to roll in, the 69-year-old Republican nominee told friends at his residence, "I just can't believe it."

Shortly after 8 p.m. PST Reagan received a congratulatory telephone call from Sen. Edward M. Kennedy (D-Mass), whom he had freely quoted in his campaign against Carter.

"Well, thank you very much," Reagan responded warmly.

Then he saw on television that independent candidate John B. Anderson was receiving enough votes to qualify for federal matching funds.

"Oh, good," Reagan said.

Joining Reagan in his suite, as he accepted the telephoned congratulations of his national chairman, Paul D. Laxalt of Nevada, who won his own reelection to the Senate tonight, was Reagan's older brother, Neil.

"I've been waiting for some numbers from Tampico and Dixon," Reagan told his older brother in a reference to their boyhood home in Illinois.

All evening long, as the Reagan landslide grew, the congratulatory telephone calls rolled in to the candidate's suite.

Accepting the thanks of Ohio Gov. James J. Rhodes, who had campaigned tirelessly for him, Reagan said: "Jim, it's looking so good it's scary."

And to another strong Reagan campaigner, Gov. Bill Clements of Texas, Reagan said, "I feel just great -- this is unbelievable, isn't it?"

And, finally, in a telephone message to Washington supporters, Reagan referred to his victory as one of the greatest in history, and added: "It looks like something big is happening to this country."

Earlier today, the candidate was outwardly cautious as he and his wife voted here in their neighborhood in a precinct whose other famous residents include Lawrence Welk and Sylvester Stallone. The expensive homes which are common-place here are mostly the residences of executives and celebrities, and are a far cry from the working-class communities where Reagan persistently sought votes in the general election campaign.

Reagan, pausing outside a flag-bedecked home that was his polling place, was asked whether he though he had won the election.

"You know, I'm too superstitious to answer anything like that," he replied.

"Cautiously optimistic," added a smiling Nancy Reagan, using a line her husband had almost exhausted on various GOP primary election days this year.

The Reagans voted in mid-morning amid a crush of well-wishers and television cameras. Then the candidate had a haircut and spent the afternoon resting before a dinner with close friends and a scheduled televised appearance before supporters in a hotel ballroom.

The precinct where the Reagans voted is dependably Republican. Two of the Reagans registered here, however, are not members of the GOP. The son, Ron, a New York ballet dancer, is registered as an independent, while the daughter, Patti, is listed as an American Independent.

Inside the polling place, the Reagans were beseiged with requests from pollwatchers to autograph books and pictures. When a reporter asked Reagan whom he had voted for, he responded with a grin, "Nancy."

Entering the black limousine that carried him about the city throughout the day, Reagan gave his wife a long kiss. A friend asked her if she was optimistic about the outcome, and she replied, "I'll be glad when the day is over."

Reagan's campaign unexpectedly had been extended Monday when a drifting ocean fog abruptly covered the runways at Los Angeles International Airport and forced the Reagan campaign plane, "Leadership 80," to land in Burbank. The plane was en route from San Diego, where Reagan presided at a final, patriotic rally at which the candidate interrupted his speech to tell a heckler to "shut up."

The rally ended with a fireworks display, which included the lighting of a gigantic American flag and the singing of "God Bless America," led by the Reagans from a makeshift stage.

The Burbank landing added an hour to the 16-hour cammpaign day of the 69-year-old GOP nominee, running for the presidency for the third time.

Reagan was visibly tired as he walked through his campaign plane on the final leg of that last flight, shaking the hand of every aide and reporter aboard. Despite his fatigue, Reagan said he was "a little sad that it was ending after all this time." Nancy Reagan, whose campaign trademark has been bowling an orange down the airplane aisle on takeoff, brought a bag of oranges for the final flight Monday night. She also rolled a grapefruit down the aisle.

For the Reagans, it was the end of an odyssey that began Nov. 13, 1979, with a New York City announcement of his presidential candidacy.

At the time Reagan said he didn't "agree that our nation must resign itself to inevitable decline, yielding its proud position to other hands." In a final television speech to the voters Monday night he used a similar theme of U.S. responsibility to maintain peace.

As America voted today, plans were already under way for a transition team in Washington that is to be headed by Reagan chief of staff Ed Meese.

Reagan is to hold closed-door meetings with aides Wednesday, a news conference Thursday and is scheduled to take some time off at his remote ranch north of Santa Barbara.

One familiar figure in the campaign, former foreign policy consultant Richard V. Allen, showed up wearing a staff pin for the candidate's victory celebration today.

Allen, a Washington consultant, removed himself from the campaign after a story about purported conflicts of interest appeared in The Wall Street Journal.

As Reagan spokesman said he did not know whether Allen would be back after the election, but he said Allen did not attend the staff meeting today.