One of every five children in America in 1981 lived in a one-parent family, a 54 percent jump since 1970, the Census Bureau reported yesterday.

The figure, a reflection of increased divorce and more births out of wedlock, includes all children under age 18. The figures show that of 62.9 million such children, 48 million lived with both parents, 12.6 million with one parent and about 2.2 million with neither parent.

Although the national total was 20 percent for children in one-parent families, the proportion was much higher among blacks than among whites, a fact that experts say is a factor in blacks' high rates of poverty and welfare dependence.

About 15 percent of white children lived in one-parent families, the Census Bureau figures show. For blacks, the figure was 45 percent. In each case, the overwhelming majority lives with the mother; fewer than 10 percent of the one-parent families are headed by the father.

The census report also measures changes in the marriage age, in divorce, in the number of people living alone and in unmarried-couple households, which include a variety of arrangements (an elderly man being cared for by a nurse, for example) and, despite a dramatic increase, still make up only 2 percent of all households.

The median age at first marriage, the report shows, has increased about 1.5 years since 1970, and is now 24.8 year for men and 22.3 years for women. Another measure of the fact that people are marrying later is that 52 percent of the women between age 20 and 24 and 70 percent of the men have never married, an increase on the order of one-third since 1970.

An upward trend of divorce also continued. In 1981, the ratio of divorced persons to each 1,000 married persons living with their spouses was 109; in 1970 it was 47, and in 1960 it was 35. The ratio for blacks is about twice that for the nation as a whole, 233 to 1,000.

The number of people living alone is rising, the Census Bureau report shows, and was 18.9 million in 1981, a 75 percent jump since 1970. The bulk of these people, 7.7 million, is elderly widows or widowers; 5.9 million of them were never married; the rest are divorced or separated.

One notable phenomenon is the growth of unmarried-couple households, which have more than tripled from 523,000 in 1970 to 1.8 million in 1981. Nevertheless, the bureau emphasized that that such arrangements still only involve a tiny proportion of the U.S. population.

Despite all these trends toward dissolution of marriage and looser family arrangements, census figures published elsewhere show that the family headed by a married couple is still the primary living arrangement for Americans--and by a very large margin.

About 74 percent of the population of the United States lived in a family headed by a married couple in 1980, these figures show.