Nearly one of every five blacks is on welfare, according to figures derived from a new study of the the nation's largest cash welfare program, Aid to Families with Dependent Children.

The statistics also indicate that about 40 percent of all black families with children under 18 are getting AFDC benefits, compared with 6.8 percent of white families with children.

Even so, there are more white beneficiaries than black, because whites make up such a predominant share of the national population.

The study, published in the latest issue of the Social Security Bulletin, sketches the characteristics of 3.4 million families receiving AFDC benefits in March, 1979.

The high proportion of blacks on welfare, particularly among families with children, reflects severe poverty among blacks, resulting from higher unemployment rates than for whites, generally lower income and the rapid rise in one-parent families that now constitute two-fifths of all black families with children.

The study shows the rapid growth of the AFDC program over the postwar era. In 1959 there were 773,000 families on AFDC, in 1969, 1.6 million families, and in 1979, 3.4 million families containing 10.4 million people, more than two-thirds of them children.

Other data from the study:

* The average recipient family declined from 4.1 persons in 1969 to 3.0 in 1979.

* Eighty percent of all AFDC families lived in metropolitan areas, and nearly half in a large central city. One-fifth of the AFDC families lived in six big cities: New York, Los Angeles, Chicago, Philadelphia, Detroit and Houston.

* Women headed four-fifths of all AFDC families.

* Families who were receiving assistance at the time of the survey had been on the rolls for a median period of 29 continuous months.

* Of the 7.2 million children on the rolls, more than one-third were under 6 and another 48 percent were from 6 to 14. Marital breakup--divorce or separation--was the reason for the child's eligibility 45 percent of the time, and lack of a marriage tie 38 percent of the time.

* Nationwide, the average monthly amount the states estimated was needed to sustain a parent and two children in 1979 was $365. The average state welfare payment for such a family was $299.

* The families were 40.4 percent white, 43.1 percent black, 13.6 percent of Hispanic origin and the rest American Indian, Asian and other groups. The category "Hispanic" is not a racial category, but refers to those who identify themselves as Hispanic whether black or white; most of the Hispanic families were actually white. If Hispanics are distributed among other groups according to race, then white families would make up 51.7 percent of the welfare families and blacks 43.9 percent.

Calculations by The Washington Post, comparing the figures in the study with general population and family statistics from the Census Bureau for 1979, show that the white families on AFDC (including white Hispanics) constituted 6.8 percent of all white families with children under 18; the black families (including black Hispanics), 40.8 percent of all black families with children under 18, and the Hispanics (if isolated as a separate group) about 25 percent of all Hispanic families with children under 18