President Reagan's first substantive act in office -- to impose a freeze on federal hiring -- is still being converted into precise regulations which are expected to be issued late this week or early next, government officials said yesterday.

The Reagan freeze replaces one put into effect by Jimmy Carter. Carter's controls on federal hiring helped reduce the number of full-time federal employes (civilians, not members of the armed forces) by 45,100 during the four years of his administration. The government now employs about 1.86 million civilians.

Reagan's executive order seems to go further than Carter's, but its actual impact will depend on the implementing regulations. The order was necessary, Reagan said, because the federal budget is "out of control."

Federal employment has been declining steadily since the late 1960s when measured either as a percentage of total employment in the country or on a per-citizen basis. Currently federal employes represent 2.8 percent of all workers in the country, and there are about 12 1/2 federal employes for every 1000 Americans. In 1952 there were 2.6 million federal employes, more than 16 per 1,000 citizens.

Compensation of federal employes is a smaller percentage of the budget than commonly believed -- an estimated $57.5 billion next year, or about 8 percent of the $739.3 billion total.

If the Reagan administration could cut federal employment by another 10 percent -- something government officials say could only be done by significantly cutting back either the number of government programs or their effectiveness -- sayings to the Treatury would be about $6 billion. That's about a third of the annual budget for Medicaid.