A total of 1,828 people nationwide were interviewed by telephone from Jan. 23 to Jan. 28 in the latest Washington Post poll. Of those interviewed, 1,358 said they were registered to vote.

Respondents were selected at random and the results were weighted slightly by age, sex, race and education to match the most recent U.S. Census Bureau figures.

Theoretically, the margin of error based on the entire sample is about 2.5 percent in either direction. In all, 750 of those interviewed said they were Democrats, and the theoretical margin of error on their part of the sample is about 3.7 percent. A total of 390 people polled identified themselves as Republicans, and the theoretical margin of error for figures on their part is 5 percent.

The margins of error refer to "sampling error," and do not take into account other types of error that may occur.

In a scant three months, President Carter has undergone one of the most stunning transformations imaginable: changing from a 98-pound weekling to the Charles Atlas of American politics. c

Perceived by many last November as a president who just couldn't cut it, he is now overwhelmingly viewed as deserving more credit than he is getting.

Carter is trusted, his character admired, his policy decisions supported. Huge majorities think that no one around can do a better job of handling the nation's most excruciating problem: obtaining the return of American hostages in Iran.

Widely regarded last fall as a likely one-term president, Carter now stands in an awesome position in his drive for reelection. He holds a lead of more than 2 to 1 over Sen. Edward M. Kennedy of Massachusetts for the Democratic nomination; he holds similar leads, give or take a little, over the chief Republican contender.

These are among the chief findings of a new Washington Post poll conducted poll, of course, cannot predict whether Carter will maintain his standing or take a tumble in the weeks and months ahead. But it can depict how he got there.

In essence, the 1,828 people interviewed -- a cross section of the nation -- give every impression of being severely jolted by tremors abroad and looking for a way to forestall an earthquake. And the way, at least in their president perception, is to rally around the president.

The charged atmosphere has led to a massive reappraisal of Carter. In a Post poll taken Nov. 1 to 12, as Carter was beginning his climb, people were asked which statement they agreed with more: "Jimmy Carter just can't seem to cut it as president," or "Jimmy Carter is better president than he is getting credit for."

At that time, 38 percent said Carter "can't cut it," and 43 percent said he deserved more credit. When the question was repeated in the new poll, 22 percent said Carter "can't cut it," and 65 percent said he deserves more credit.

In another test of overall popularity, The Post asked citizens to rate Carter's performance on a scale of zero to 10, with zero being the most unfavorable rating and 10 the most favorable. In November, Carter scored an average of 5.0; in the new poll he scored 6.4 -- an increase roughly equivalent to a gain of 14 points in a Gallup poll.

The concern over foreign affairs and overall respect for Carter's handling of them has done more than raise the president's popularity. It has absolutely dulled what had been the nation's number one concern, inflation, as a campaign issue.

People today are every bit as fearful of inflation as they have been, and more so. In the November poll, 24 percent of those interviewed said they thought things were getting worse for them financially. By an overwhelming margin, they wanted Carter turned out of office.

In the new poll, 36 percent said they thought things were getting worse for them financially. Now, however, they don't seem to want to take that out on Carter. They support him for president by a margin only slightly smaller than do those who see their personal fortunes getting better or staying the same.

Political observers long have maintained that the state of the nation's economy is of paramount importance in a presidential election, and many now insist that before long inflation again will be leading campaign issue against Carter.

Part of Carter's burst in the polls may be attributed to the floundering campaign of Kennedy. Kennedy now trails Carter among Democrats by 58 percent to 5 percent. Last summer he led Carter by that much; as recently as November, Kennedy led by 49 to 27 in a Post poll.

In the new poll, 18 percent of all interviewed said they could not support Kennedy under any circumstances. Asked why, their volunteered responses indicate that anti-Kennedy feeling is based much more on personal and than political sentiment: 31 percent cited Chappaquidick or Kennedy's personal life; 25 percent said he was just running on his name; 16 percent said they did not trust him in a crisis; 20 percent said they felt he was too liberal or a big spender.

In contrast, 5 percent said they would vote for Carter under any circumstances.

In a series of five questions dealing with personal character and political effectiveness, the 750 Democrats polled were asked to draw comparisons between Carter, Kennedy and California Gov. Edmund G. (Jerry) Brown.

In only one of those questions -- ability to deal effectively with Congress -- did Kennedy rate higher than Carter. Forty-six percent rated Kennedy the most effective at that; 34 percent chose Carter, 3 percent chose Brown.

The poll suggests that if events get back to "normal" during the election campaign, among Carter's chief areas of vulnerability will be his perceived inability to deal with Congress, a symptom of overall complants about his leadership, as well as widespread concern over inflation.

Right now, however, Carter bests Kennedy on every other measure tested. He was cited by 54 to 25 percent over Kennedy as best able to deal with hostile foreign governments, by a 59 to 24 as the one who best sets an example of how our leaders should behave by 49 to 25 as having the best understanding of "the problems of people like you," and a by 52 to 32 as the one those interviewed would most like to meet and talk to if they had the opportunity.

Brown drew no more than 5 percent support on any of those questions, and only 4 percent of the Democrats interviewed listed him as their preferred nominee over Kennedy and Carter. Eighteen percent said they would not vote for Brown under any circumstances.

In the Republican race, Ronald Reagan still leads nationwide, with 36 percent of the Republicans interviewed by the Post favoring him. But he is closely trailed by George Bush, at 26 percent. Lagging far behind are Howard Baker with 11 percent and John Connally with 5 percent.

Reagan, who led Carter in trial heats at times last year but now trails him by 65 percent to 30 percent in the Post poll, appears to have been hurt by three factors: his age, the importance of foreign affairs, and the national prominence given Bush after his win in the Iowa caucuses.

A total of 28 percent of the public at large and 22 percent of the Republicans interviewed said they feel Reagans is too old to be a president.

The foreign affairs problems for Reagan is a tricky one. When asked directly which Republican candidate is best able to deal with hostile governments, more Republicans interviewed selected Reagan than any other GOP candidate, although Bush was not far behind.

But when asked that question in a slightly different way, Reagan appeared very vulnerable. People were asked which they regard as most important in a president at this time: ability to deal with hostile foreign governments or ability to deal effecitively with problems at home.

The largets single group of people, 46 percent, said the nation needs a president who can do both. Among that group and among those whose main concerns was domestic problems, Reagan far outpaced the rest of the Republicans.

But among those who cited the need for someone who could deal with foreign affairs as the nation's main need, Reagan did comparatively poorly. If ability to deal with hostile foreign governments continues to grow in importance as a campaign issue, the poll suggests, voters may find themselves ever so subtly moving away from Reagan.

In effect, the rise of George Bush appears to be a demonstration of how powerful an effect a single event such as the Iowa precinct caucuses may have on the presidential race. Bush drew only 5 percent support from Republicans in the Post's November poll, far behind Baker and Connally, as well as Reagan.

The main question for the Republicans is this: If Iowa propelled Bush as far as it did, what will New Hampshire do for him -- or for Reagan, or, perhaps, for the other candidates?