Federal workers who now park free at the office will began paying half the commercial rate next month, ranging from a low of $5.50 in Falls Church to $45 a month in downtown Washington.

The new rates set by the General Services Administration on a building-by-building basis nationwide are supposed to approximate half the commerical parking fee charged at nearby lots. Under President Carter's program to elimate most free parking for employes at government agencies, workers will begin paying the half rate next month and full monthly parking fees by November 1981.

According to a computer printout of the new rates obtained by this column the highest fees will be charged employes of the Electronic Funds Transfer Commission and National Commission on Library information, relatively small outfits at 1825 K St. NW, and 1000 Connecticut Ave. They will be charged $45 a month beginning in November.

The lowest rate in the area ill be charged U.S. workers at several facilities in Fall Church. They will pay fees of from $5.50 to $6.

Here is a rundown of some of the new rates in major buildings:

Court of Claims, $42.50 a month, New Executive Office, $40; GOP's Navy Yard Annex, $12.50; U.S. Tax Court, $30, Hurbert Humphrey Building, and Labor Department, $30; Great Plaza, 14th and C Streets NW, $25; J. Edgar Hoover FBI Building, $32.50. HUD Building, and Federal Building at 800 Independence Ave. SW, $30.

Federal Building, 600 Independence Ave. Sw, $30; Mary E. Switzer Memorial Building, $27.50; Gen-Accounting Office, $25; New State Department, $27.50; General Services Administration at Seventh and D streets SW, $30; Old Post Office Building, $27.50; Pension Building, $20; Federal Building, 12th Street and Pennsylvania Avenue NW, $27.50 Justice Department, $30 and $27.50, GSA main bulding, $32.50; Commerce Department, $30 and $27.50; Federal Trade Commission, $30. Courthouse, Constitution Avenue and John Marshall Place, $30; Agriculture Department, $27.50. FOB 6, at Fourth and C streets SW,$30 and $27.50.

The Pentagon, about $9.50 for more than 10,000 outside spaces and slightly over $12 for 321 inside spaces; Federal Building NO. 2 at Columbia Pike and Old Ridge Road will charge just over $9 per month for more than 1,100 spaces.

Westwood Building in Bethesda, $8.25 a month for 700 spaces; $16.25 for the Federal Building at 7550 Wisconsin Ave. in Bethesda.

The Scuderi Building in Hillcrest Heights, $8.25; and $8.25 at the World Weather Building; $8.50 at the Presidential Building, Hyattsville.

The Washington Science Center in Rockville will charge $8.25; Parklawn Office Building, approximately $15 for inside parking and just over $10 monthly for outside parking.

Federal Building No. 2 in Suitland, $6 a month for 2,140 spaces, Oceanographic Building on Silver Hill Road,$6.

Workers at the Custom House at Gay and Lombard streets, Baltimore, will pay nearly $22 a month, and those at the Courthouse at Calvert and Fayette streets, will pay $25; George H. Fallon Building in Balitmore, $30; Social Security Workers at Woodlawn, between $10 and $6.

Workers in most of the Navy Annex parking areas -- With several thousand parking spaces -- will generally pay just over $16 a month. Customs Service employes at 1301 Constitution Ave. NW, will pay $30 for inside parking, slightly less for outside parking; NASSIF Building, 400 Seventh St., $30; 1919 M St. NW (leased building), $32.50; Page Building 3300 Whitehaven, Georgetown, $20.

Under the GSA guidelines, there is not parking charge if agencies can prove commericial parking in their areas cost less than $10 a month, or if there is no commerical parking. For example, as this column reported last month, the Central Intelligence Agency in Langley, asked for an exemption on the ground that it was remote -- on purpose -- from regular parking, and because most employes have to drive to work. Parking will continue to be free at the CIA.