More than 34 million retired persons receiving federal pensions and Social Security will get a cost-of-living raise in January of slightly more than 3 percent.

The raise will reflect the average rise in living costs from the third quarter of 1983 to the third quarter of 1984.

The exact amount of the increase will depend on the Consumer Price Index of urban wage earners, a figure that will be released Oct. 24. The increases will go into effect in December and show up in checks mailed for delivery in January.

Those who can look for the increase include people drawing Social Security benefits and 1.4 million retired federal workers, 400,000 survivors of federal retirees, 500,000 military retirees and 49,000 of their survivors.

Federal workers once got cost-of-living raises every two years. But after several years of double-digit inflation, Congress found that system too expensive.

During the first year of the Reagan administration Congress trimmed it back to a single COL adjustment each year. Last year, the adjustment due federal retirees was delayed until this January so the increase would come at the same time as raises for persons drawing Social Security.

Congress originally planned to give smaller increases to retirees who were under age 62 but abandoned that plan this year. That means that all retirees will get the same percentage raise regardless of age or income.

The increase will be automatic, and, unless Congress changes its mind again next year, will be paid each January from now on.