The nation elected Ronald Reagan its 40th president yesterday, casting an elected incumbent out of office for the first time since 1932 and propelling the conservative Republican to an overwhelming victory with support in every corner of the country.

President Carter carried only five states and the District of Columbia in yesterday's balloting, as American voters swung sharply to the right, handing Reagan 449 electoral votes in a landslide of unexpected proportions.

With 88 per cent of the vote tallied at 4 a.m., Reagan had 37,760,000 votes, or 51 per cent of the total, with Carter at 42 per cent and independent candidate Rep. John B. Anderson (R-I11.) at 6 per cent.

Union members, midwestern and Eastern voters, urban residents and even voters from Carter's own South switched in large numbers to the GOP challenger, making Carter the first Democratic incumbent to be defeated for reelection in more than 100 years.

Carter's failure to win the release of the American hostages in Iran, widespread concern over American military and economic policy, and Anderson's independent candidacy all hurt the president, election day surveys showed.

Reagan, who called his election "the most humbling moment in my life," told a Los Angeles crowd of cheering partisans that he was "determined to use this historic opportunity to change things."

"I don't believe the American people are frightened by what lies ahead," Reagan said, repeating his familiar campaign pledge to "put America back to work again."

Thanking his supporters for their efforts, Reagan said, "I will do my utmost to justify your faith."

Carter conceded the race at 9:51 p.m., telling a tearful crowd of Washington D.C. supporters, "When I was elected, I said I'd never lie to you. I can't stand here tonight and say it doesn't hurt."

Against the backdrop of the American flag, Carter said he accepted the decision of the nation's voters "though not with the same enthusiasm" that he accepted their verdict four years ago. He pledged to work closely with president-elect Reagan in hopes of the "best transition period in history."

"I didn't achieve all I set out to do, but we faced the tough issues," Carter, who won a narrow victory over incumbent Gerald Ford, told the crowd.

Anderson, who began the year as a Republican challenger to Reagan, dropped hints to another D.C. crowd that he might repeat his bid for the White House in four years.

His loss represented "a decision deferred," Anderson told the audience, which chanted "'84, '84, '84" and applauded the Illinois congressman, who finished with just enough votes to insure federal matching funds for his debt-ridden candidacy.

Anderson telephoned his congratulations to Reagan at 8:35 p.m. EST, 15 minutes before Carter sent a congratulatory telegram to the GOP nominee.

Carter's defeat was apparent even before the polls closed; presidential pollster Patrick Caddell told the incumbent yesterday morning that final surveys showed him trailing Reagan by seven to ten percentage points.