If Americans keep having children at about the rate they are now, the nation's population will grow by 14.7 million in the next 12 years, the Commerce Department said yesterday.

Current U.S. population is about 218 million and is growing by 0.8 per cent a year. If the rate stays about the same, the country will have 262.5 million people by the year 2000, the department said.

The projection, which assumes that young women will have an average of 2.1 children over the next few decades, is included in a 647-page compilation by the department's Cernsus Bureau and Office of Federal Statistical Policy and Standards.

Denis F. Johnston, chief author of the report, called "social Indicators 1976," said the fertility rate has recently been about 1.8 "but is now edging up." The 2.1 rate projected "is a guess," he conceded, and is the so-called "replacement" level at which a generation replaces itself but does not increase the population.

The study said the 2.1 rate would mean a population of 312 million by the year 2040.

If, however, women have an average of 2.7 children, as they did during the "baby boom" of the 1950s, the nation would grow to 287 million by the year 2000 and nearly 450 million by 2040, the study said. If the fertility level drops to 1.7 the population would be 245 million in 2000 and just under 238 million in 2040.

On basis for believing that the fertility rate will rise to 2.1 is a recent study by the National Opinion Research Center at the University of Chicago. Johnston said. It shows that in 1975 more than half - 52.5 per cent - of the people interviewed said a family with two children would be ideal. In 1972 only 43.8 per cent of a similar sample expressed the same view.

The study also forecasts a continuing decline in the size of the average family. It peaked at about 3.7 persons in 1965, dropped to 3.4 in 1975 and is expected to hit 3 by 1990.

Johnston said the general growth in affluence has meant that aging couples can afford to live by themselves and not with grown children, thus further reducing family size.

The report also noted that by 1975 more than half of black families and nearly 60 per cent of white families had only two or three members, "Between 1960 and 1975 the proportion of large white families (six persons or more) declined from 12 to 9 per cent, while the corresponding proportion among black families dropped from 26 to 18 per cent," it added.

In 1975 more than 28 per cent of people aged 65 or older lived alone. Nearly 15 per cent of men and 38 per cent of women in that age bracket were alone, according to a Census study.

The same study also documented the rise in the number of families headed by women without husbands. Such families made up 35.3 per cent of all black families and 10.5 per cent of all white families in 1975. In 1960 they were only 21 per cent of black families and 8 per cent of white families.

The report cited another trend - the aging of the American population - and predicted that it would continue.

In 1940 only 7.1 per cent of the population was 65 or older. In 1970 the percentage had risen to 10.3 and by the year 2000 it is expected to be more than 12, the report said.

"The proportion of the population under 20 years of age is expected to decline to 30 per cent in 2000 from the 1970 level of 38 per cent," the Commerce Department said in a news release on the study.

The study, which includes hundreds of government and private research reports, contains a mass of statistics, many of them previously published separately, on various aspects of Amercian life.Among the findings:

Between 1953 and 1974 the annual number of divorces and annulments increased 2.5 times and the number of children involved rose more than three times.

The number of Social Security beneficiaries rose from 3.5 million in 1950 to 32.1 million in 1975, up from 2.3 per cent of the population to 15 per cent,

In 1940 about 45 per cent of the nation's housing units did not have full indoor plumbing.In 1974 only 3 per cent did not have it.

Infant mortality has declined in recent years, but the U.S. rate is still higher than that of several other industrial nations. The U.S. rate went from nearly 25 per 1,000 live births in 1965 to 16.7 per 1,000 in 1974. The rate in Finland is about 12; in Japan 11.3, and in Sweden just under 10.

From 1960 to 1975 the rate of violent crimes tripled and the rate of crimes against property went up almost as much - 2.8 times. Robbery increased at the highest rate - in 1975 there were 3.6 times as many robberies as there were in 1960.

The ratio of non-workers, including children under 16 who are not in the work force anyway, to workers dropped from a peak of 151 to 100 in 1965 to 123 to 100 a decade later.

Statistician Johnson said the reasons are that more woman are entering the labor market (they made up 46 per cent of the work force in 1975) and there are fewer children under 16.

"There is increasing dependency among the aged," he said, "but we're seeing a greater reduction in youth dependency than an increase in aged dependents, partly because the elderly have more income then they did a decade ago."

Median family income in 1975 was $12,570, nearly double that, of the late 1940s and about $1,700 higher than in 1965.