Washington area schools will lose almost $20 million in impact aid for educating children of federal employes this school year as a result of Reagan administration budget cuts, the Department of Education said yesterday.

The figures, which weren't available until this week, confirmed the warnings U.S. officials gave local school officials last summer when they cautioned to expect drastic reductions in impact aid for the current school year. Congress, at Reagan's urging, slashed the impact aid budget from last year's $706 million to $455 million.

Fairfax County, which was expecting to be hit hard by the reductions, could lose all its impact funds unless it abandons plans to charge tuition for educating children who live on the Fort Belvoir Army base, Education officials threatened yesterday. Under the newly announced figures, Fairfax, which expected to receive $5.8 million in impact aid, will get $3.4 million.

Officials in other jurisdictions said yesterday they were relieved to know the extent of the cuts. "We've been playing Russian roulette with this," said Eliott Robertson, assistant superintendent for budget and facilities in the Prince George's County school system. "Each year we've gotten less and less in impact aid, so two years ago we began to budget nothing for it."

Prince George's will get $2.5 million this year, down from $3.9 million last year. The District of Columbia also will get $2.5 million, a drop from $3.3 million, and Montgomery County will receive $600,000, down from $1.9 million.

Other area schools and the decreases they face are: Alexandria, $364,000, down 28 percent; Arlington, $470,000, down 42 percent; Prince William County, $1.2 million, down 25 percent; Loudoun County, $39,900, down 77 percent, and Fauquier County, $166,000, down 28 percent.

Impact aid reimburses local school districts for part of the cost of educating dependents of employes stationed at federal installations. Every president since Eisenhower has attempted to eliminate much of the impact aid program. Reagan is expected next week to recommend even sharper cuts, freezing future payments at $284 million indefinitely, according to budget documents.

The federal impact cuts disclosed yesterday will cost Virginia schools $11.2 million, one-third of last year's $32.8 million allotment, said William Stormer, director of the Education Department's impact aid division. Maryland will lose $7.6 million of last year's $17.9 million payment.

Most school districts in Maryland and Virginia already have asked their local governments to make up the difference in lost federal money with local tax dollars.

Fairfax County supervisors earlier this year set aside $2.5 million in a contingency fund to help the schools face such a shortfall in federal aid. The schools probably will have to use virtually all of those funds, said John Hess, assistant Fairfax superintendent for financial services.

Department of Education officials said the final payments to school districts could vary slightly, pending budget revisions by Congress or changes in local school district enrollments. Stormer said school systems will begin receiving impact aid payments during the next five months for the current school year.