Half of American women work outside the home, and they are relying increasingly on day care centers and paid babysitters, rather than relatives, to look after their small children, the Census Bureau reported yesterday.

In all, 48.7 percent of the children of full-time working mothers are cared for in day care centers or by babysitters who are not related to the child. The figure has doubled since 1958, the report said.

Fathers took care of 10.6 percent of the children, down from 14.7 in 1958.

Once, the overwhelming majority of women stayed home and took care of their children, but in the past 40 years they have shifted to paid employment in remarkable numbers. In 1980, according to the report, 44 million women, or more than half of those over 16, were in the labor force, compared to only a quarter in 1940.

Moreover, this massive swing of women to work outside the home occurred even among those with small children: 45 percent of all wives with pre-school children were working in 1980, nearly four times the percentage in 1950.

As a result, according to the report, there were 7.5 million pre-school children with working mothers in 1980; in 1990, it was projected, there will be 10 million.

Who minds these kids while their mothers are away?

Here, too, there has been a big shift in recent years, according to the report, which was written by Martin O'Connell, Marjorie Lueck and Ann C. Orr.

As recently as 1958, the report said, 57 percent of the pre-school children of full-time working mothers were cared for in their own homes, usually by the child's father or by relatives--an aunt, grandparent or older child.

No longer. With greater dispersion of American families, fewer relatives are available in the home or immediate neighborhood; and with lower birthrates, families are smaller today and there are less likely to be older children around.

Moreover, O'Connell said in an interview, changes in the labor force are reducing the number of blue-collar jobs that have enough variation in time schedules to allow fathers to be home while the mother is away.

As a result, in 1977 only 29 percent of pre-school children of full-time working women were cared for in the home while their mothers were out on the job, usually by the father or another relative but sometimes by a non-relative hired to come in.

While the proportion of children cared for in the home dropped sharply, the share taken care of in other people's houses, sometimes relatives and sometimes just a person paid to do it, almost doubled from 1958 to 1977, reaching 47 percent. At the same time, those who attended organized day care centers almost tripled, to 15 percent. The remaining 8 percent stayed with the mother where she was working.

The study said higher-income families tended to use day care centers, which can cost thousands of dollars a year. Lower-income families tended to make more at-home arrangements.

The report said that in many countries of northern Europe, women's labor force participation rates are even higher than in the United States. In Sweden, the report said, there had been heavy governmental emphasis on providing day care facilities and as a result, while a fair proportion of children were cared for in the home, about half went to public nurseries and child care centers.