The federal government continues to be the largest single user of computers in the nation although the private sector is increasing its use at a faster pace, according to an industry study to be released today. The study also notes that Japan is gaining on the United States, which is the Number One exporter of computers worldwide.

Although the federal government accounted last year for the highest share of computer usage in the United States - 6 per cent - almost all computers were utilized by the government when they became generally available in the 1950s.

In its current issue, Business Week magazine says the computer industry rate of growth has stabilized after two decades of prime expansion. The magazine quotes analysis as predicting annual growth in sales in the range of 10 to 20 per cent.

Last year, some $38.4 billion was spent on the estimated 229,000 computer installations in the U.S. on computer goods and services. Of this figure, $20 billion went for machinery and services, and the rest was spent on related salaries of computer operators and programmers, as well as overhead.

Congress spent $25 millin last year for its computer services, including electronic voting, and scheduling of committee meetings, hearing transcripts, and answering constituents mail, CBS reported recently.

Rep. David Stockman (R-Mich) rents his own small computer, at a cost of $19,000 a year, to answer mail. He also serves on a policy group that is seeking among other things, to prevent abuses such as using computers for political advantage. Computers facilitate direct-mail electioneering.

In the federal government, the biggest user remains the Department of Defense, with 46 per cent of the computer use. Contrary to popular thought, the National Aeronautics and Space Administration - with its pushbutton interplanetary travel - is only third, with 13 per cent. Second in the survey based on data from fiscal year 1976 was the Energy Research and Development Administration, which had to tackle such ponderous problems as estimating how many trillions of cubic feet of reserves of natural gas are left in any given year.

In the private sector, the insurance and banking industries have become the most computerized, although manufacturing spends the most on computer equipment and services, according to 'Information Processing in the United States: A Quantitative Summary." The document was prepared by the American Federation of Information Processing Societis, a trade organization.

In 1976, U.S. computer equipment manufacturers accounted for 87 per cent of the sale of the world's computers, by value. This represented approximately half of the those firms' revenues. Hut by 1981, the American share is expected to be cut to 81 per cent of the international market by foreign competition, especially from Japan.

The areas growing most quickly are minicomputer systems, used primarily in regulating manufacturing processes, and digital electronic technology, in the form of microprocessors and integrated circuit "chips."