Business contributions to social, cultural and educational activities are unlikely to increase significantly despite the Reagan administration's call for private giving to fill many of the gaps left by federal budget-cutting.

The Conference Board, a non-profit business research institute, reported today that a survey of more than 400 major corporations--which accounted for a lion's share of the $2.7 billion in corporate philanthropy last year--showed that only 6 percent planned to increase their contributions to offset some of the federal budget cuts.

In his State of the Union address Tuesday, President Reagan again called on private groups to replace the government in funding and running many social programs.

Although more than 60 percent of the companies planned to spend more on philanthropy this year, the report said the increased giving is a "normal" year-to-year increase related to higher profits and inflation.

E. Patrick McGuire, executive director of the Conference Board's business/government research programs, said business contributions probably will rise to $2.8 billion or $2.9 billion in 1982. He noted that for the more than 40 years that the research organization has tracked corporate giving, it has been related more to the level of profits than anything else. When profits rise, contributions rise, and when profits fall contributions do likewise.

Furthermore, he said, the study showed that few corporations are changing the direction of their giving from arts and education--traditional recipients of corporate philanthropy--to other areas heavily hit by federal cutbacks, such as job training, welfare or health.

For the most part, companies think that they are giving all that they can give comfortably and that the Reagan administration is unaware of the extent of corporate philanthropy. Furthermore, many of the programs, such as legal aid, that faced the Reagan administration ax were disliked by the business community as well. McGuire said analysts on the White House staff "probably" did not do their homework when they suggested that private voluntarism could replace many of the cutbacks in social and cultural spending advocated by the Reagan administration and enacted by Congress last August.

One corporate executive told the Conference Board, "Our company supported the president because we believed in the elimination of a number of these programs. Naturally we're not too enthused about continuing the programs and shifting the burden to the corporate sector."

By far the largest source of private philanthropy is individuals, who gave $39 billion in contributions last year, more than half to churches. Foundations provided $2.4 billion.

McGuire said the main source of business philanthropy is large companies. Many medium and small companies give little or nothing. He said that the Conference Board's contacts with private agencies indicates that few, if any, of the non-givers have been moved by the president's call for voluntarism.

McGuire noted that traditionally the biggest source of volunteer labor in the United States has been the housewife. But the number of wives working full time has been rising sharply--41 percent worked in 1970 compared with 51 percent in 1980 --and, as a result, the pool of volunteer labor has shrunk.

He said that cuts in the maximum personal income tax rate make it less lucrative for wealthy taxpayers to make contributions. Furthermore, McGuire said foundations are less able to step up giving than they would have been a decade ago because inflation has eroded their assets.

McGuire said that in many cases companies are reluctant to dispense funds to many social programs because they feel incompetent or unwilling to be "funds dispensers." Corporate executives feel social decisions should be made by elected representatives.