The population of the Washington area, which soared during the 1960's and moved upward slowly for the next five years, has stopped growing since 1975, according to U.S. Census Bureau estimates just made available.

The latest census figures - wstimates for July, 1977 - place the area's population at 3,028,100. The total is 5,100 less than a year earlier but only 1,200 more than in 1975 - a fluctuation so slight that it falls within the survey's margin of error, indicating that no signifaicant change occurred.

During the 1960's, the population the Washington metropolitan area increased by 37.8 percent. It rose by 4.1 percent from 1970 to 1975.

"I think we're seeing a maturation of the Washington area," said Thomas Muller, a reseracher for the Urban Institute. "It's no longer the major growth center it used to be, but there's no sign of decline. We seem to be into a time of stability."

Even though the population is steady, the number of households in the area is ontinuing to increase substantially, creating the demand for a housing boom as more singles, young couples and elderly live on their own.

Also, just outside the metropolitan area there is rapid population growth, the Census Bureau reported, in such "fringe" counties as Howard Maryland and Stafford in Virginia.

"The Washington area isn't stagnating," said George W. Grier, a demographer who heads a consulting firm. "There's a whole shift going on in the dynamics of the area's population. The same thing is happening nationally - more small households, more development on the fringes - but I think it's probably magnified here."

Of the country's 20 largest matropolitan areas only four, all in the burgeoning Sunbelt, have had substantial population growth in the 1970s. They are San Diego, Houston, Dallas and Atlanta.

In almost all the others, including Washington, more people have moved away from the metropolitan areas than moved into them, a major reversal of historic migration paths.

Since 1970, about 64,000 more people left the Washington area than settled here. About 40,000 of this net migration loss occurred between 1975 and 1977, according to the Census Bureau estimates.

The population here remained stable since 1975 and grew slightly in the five years before then only because there were more births over deaths, a phenomenon demographers call natural increase. However, births have declined so sharply that even this natural increase has been much less in recent years than it was during the 1960s.

Within the Washington area the new figures indicate major changes are taking place:

The population of the District of Columbia is continuing to deop rapidly, falling from 711,500 in 1975 to 685,000 in 1977.

A slow but steady decrease has occurred in PrinceGeorge's County since 1972. Prince George's is gaining black families from the District but is losing more whites - most of them, census experts believe, to counties farther from Washington in Maryland, such as Charles and Anne Arundel.

The Prince George's estimate for 1977-672,100-was 21,000 less than the peak reached in 1972.

Fairfax County is having the most rapid growth of any of the major suburban counties. Its population reached 537,700 in 1977, the Census Bureau said, up 23,000 in two years and 83,000 since 1970.

These estimates are disputed by Fairfax officials who believe growth has been even greater, but census experts say the local demographers have not taken proper account of shrinking household size, in making their estimates.

Proportionately, the greatest growth in the metropolitan area has occured in the three counties farthest from Washington-Loudoun and Prince William in Virginia and Charles County in Maryland. In Loudoun and Charles groth during the 1970s has been faster than it was during the 1960s.

The population of Montgomery County was unchanged at about 572,000 from 1975 to 1977 after modest increases during first half of the 1970s.

Alexandria's population continuted to drop slightly - down to 104,800 in 1977, while the population of Arlington stabilized at about 155,000 after a sharp drop during the previous half-decade.

"The inner suburbs are aging"Grier remarked. "The kids of the baby-boom years have grown up and moved out. Some of the houses have the same owners but there are fewer people living in them. Where there are mew families, they don't have nearly as many kids as the ones used to have."

Grier said that because of the high prives of houses close to Washingtonmany middle-income families far from the city or just outside the metropolitan area.

In some cases the moves require long-distance commuting by automobile to jobs in Washington, but Grier said many residents of the metropolitan fringe are employed at mew job centres in the suburbs, such as Gaithersburg or Tyson's Corner.

From 1970 to 1977, the number of workers employed in Washington rose by just 11,000, according to the D.C. Department of Labor. Employment in the suburbs, the department said, increased by 204,000.

"Despite all the talk about the energy crisis," said Muller, of the Urban Institute, "the population and the jobs are contunuing to move out from the center in all metropolitan areas, including here . . . The price of houses is so much lower [in the idstant counties] that even if gas hits $1 a gallon, it will still pay to move to them."The new census figures show that Howard County, Md, with a 77 percent population increase since 1973, has been the fastest-growing county during the current decade in either Maryland or Virginea. Most of Howard's growth is cintered around Columbia, many of whose residents drive down Route 29 to jobs in Washington or its suburbs.

In Virginia, the fastest-growing county has been Spottsylvania around Fresericksburg which sends commuters here on Interstate Route 95. It has a 68 percent population increase in seven years.

Overall, the number of persons employed in the Washington metropolitan area rose by 12.8 percent from 1970 to 1975, while the area's population rose by 4.1 percint. From 1975 to 1977,employment increased by another 4.7 percint even though population was unchanged.

Muller said the main factors in the employment increase were the large number of people, born in the baby-boom years of the 1950s, who entered the work force and the growing proportion of women holding paid jobs.

The maturing of the children of the 1950s also is a prime reason for the great growth in households, said Fredcrick Cavanaugh, chief of local population estimates for the Census Bureau along with the increased number of elderly people living alone.

From 1970, the number of hoseholds in the Washington area increased by 25 percent, the Census Bureau said. Average household size decreased, according to census figures, from 3.1 percent to 2.7.