Population growth in the Washington area, which surged during the 1960s, has slowed to a trickle during the past four years, according to new U.S. Census Bureau estimates.

From 1972 to 1976, the Census Bureau said, the population of the metropolitan area rose by just 24,500 to 3,035,900. The average gain was just over 6,100 a year, compared to average growth 51,000 a year between 1970 and 1972, and an average of 78,400 a year during the boom years of the 1960s.

The drastic slowdown, demographers say, probably is accounted for by three major trends - a sharp drop in the birth-rate, the shift of U.S. population growth toward the South and West, and the development of rural areas and small towns, many of them on the metropolitan fringe.

Overall, more people are now leaving the Washington area than moving into it, which means that all the population growth that has occured here is accounted for by the surplus of local births over deaths, which demographers call natural increase.

A similar change - from booming growth to slow growth or population decline - is taking place in metropolitan areas throughout the country. Indeed, most of the largest metropolitant centers, including New York, Chicago, and Los Angeles, have lost population during the last half decade.

"Washington is still one of the few large metropolitan areas that's growing," said Frederick Cavanaugh, chief of the local area estimates branch of the Census Bureau, "but it's not by very much."

Within the Washington area, the sharpest change in population trends has been in Prince George's County.

During the 1960s, Prince George's grew by 85 per cent - a faster rate than any other large county in the United States except for Orange County in southern California. Growth slowed but continued for two more years after the 1970 census, but since 1972 the population of Prince George's has dropped by 18,200 - 2.6 per cent decline. Last year, the Census Bureau said, it was down to 675,500.

Two close in Virgin suburbs - Arlington and Alexandria - also have had population losses during the 1970s for the first time in the 20th Century, while the District of Columbia's population drop which began in the 1950s, has accelerated.

Meanwhile, Montgomery and Fairfax, the area's two wealthiest suburban counties, have continued to grow but much less quickly than during the 1960s.

The only counties in the metropolitan area to maintain rapid growth are the three farthest from Washington - Loudoun and Prince William in Virginia and Charles County in Maryland. Since 1970, all of them have grown at about 6 per cent a year, with growth in Loudoun and Charles being even faster than it was during the 1960s.

Counties just outside the metropolitan area also have grown rapidly, the Census Bureau said, particularly Stafford and Spottsylvania counties, on Interstate Route 95 in Virginia, and Calvert and Howard counties in Maryland. The new census figures show that Howard, with the booming new town of Columbia on Rte. 29, has been the fastest growing county in either Maryland or Virginia with a 66 per cent population increase over the past six years.

Cavanaugh suggested that the growth of the fringe counties, which at the moment have relatively low housing prices and improved highway connections to jobs, probably had diverted population away from the metropolitan area.

In Prince George's, the population turnabout after 1972 probably involved three factors, Cavanaugh and several other experts said - the sewer moratorium, a relatively high level of taxes, and the massive court-ordered busing program for school desegregation, which went into effect in January, 1973, and was accompanied by a sharp drop in white enrollment.

However, population growth also slowed substantially in both Fairfax and Montgomery counties after 1972. Indeed, Fairfax has grown by the same amount (35,000) in the four years since 1972 as it did during the four years since 1972 as it did during the two years before it.

The population loss in Arlington - 20,800 since 1970 or an 11.9 per cent decline - has been the steepest in the area, sharper even than the 7.3 per cent post-1970 drop in Washington, with which Arlington shares many characteristics of central cities.

In Alexandria, the loss since 1970 has amounted to 2.5 per cent. However, the new census estimates indicate that Alexandria has gained population slightly since 1975, while Arlington's rate of loss has leveled off.

On the other hand, the population loss in Prince George's county has been running at a steady 4,000 to 5,000 a year since 1972, while the District of Columbia has been losing about 10,000 a year.