Enrollment in public schools in the Washington metropolitan area have declined by 52.622 over the last six years, but school budgets have gone up in every jurisdiction during the ame period.

Although the most drastic decrease in the number of students has occured in the District of Columbia, where there are 19,854 fewer students enrolled this school year than in 1970 (a 14 per cent decrease), enrollment declined in every area school system last fall.

Budgets, however have soared. In Fairfax County, which opened its schools last September, with 2,270 fewer pupils than the previous spring and had then only 1 per cent more students than six years ago, the school system's operating budget is up 97 per cent over 1970.

Yesterday, Fairfax Supt. S. John Davis proposed a $286.7 million budget for the 1977-78 school year which, despite major cost-saving reductions and a lower projected enrollment, will require that the county increase its funding of county schools by $18.7 million over the current year.

Fairfax, although its enrollment was the last to peak in 1975, before joining the area-wide decline, is not alone in the large expansion of its budget. The District's operating school budget has ballooned 47 per cent in the last six years, despite the 14 per cent decrease in enrollment.

In Montgomery and Prince George's counties, where enrollments reached their highest levels in the early 1970s and later dropped 7 and 10 per cent respectively, school operating budgets are up 71 and 63 per cent, respectively, since 1970.

Arlington was the first jurisdiction to begin to lose enrollment - in 1963 - and its budget has gone up the least - 30 per cent - since 1970. Arlington has seen a 23 per cent reduction in its student body since 1970.

School budget critics say school administration costs are too hight, and they demand that savings be achieved by greater efficiency.

School officials say that while fewer babies are being born and fewer children entering kindergarten, schools built to accommodate the baby boom must still be heated, cleaned and repaired, along with the schools that are now being constructed in newly developing communities.

In explaining rising budgets, school officials also cite escalating fuel costs, higher teachers' salaries, general inflation and the need to provide expensive new programs mandated by state and federal authorities. Those programs "are always underfunded" according to Myron E. Cale, Fairfax's assistant superintendent for financial services.

In Fairfax, for example, where the school operating budget has gone up $86 million in only the last four school years, $14 million of that increase has been for federal and state-required special education programs.

In 1972, Fairfax had 370 staff members involved with special education programs and the budgeted cost was $4.3 million. Today, there are 1,074 persons working with special education programs and the cost has risen to over $18 million in the 1976-1977 school budget of $225 million.

Fairfax school officials, like those in other jurisdictions, complain about these required programs and standards. At its last meeting, the Fairfax School Board asked the state legislature to reverse a law passed last year requiring that by 1977-78 no first, second or third grade class exceed 28 pupils. This requirement, the school board staff said, will cost the Fairfax county school system on additional $2.4 million and necessitate the hiring of 205 additional teachers during the next school year.

Teachers' salaries are another inflationary item in the budget, rising 35 per cent over the last four years, and adding $28 million to the last four school budgets, Fairfax school officials say. The teachers' retirement plan, presently costing the county $7.7 million, did not exist four years ago. Health insurance for school employees costs $2.5 million more than it did in 1972. Salaries, the retirement plan and health insurance account for 54 per cent ($121 million) of this year's school budget in Fairfax ($225 million).

Oil to heat school facilities will cost an estimated $2.9 million this school year. This is $2 million more than the county spent for oil four years ago ($974,500). Maintenance of school facilities now requires $8.7 million, a $3.7 million jump over four years ago.

The remaining $75 million in this year's school budget is spent on a broad range of expenses including books, school bus operations, administrative costs and instructional materials for special programs like the sex education program, which will cost $13,500 to implement.

Fairfax school officials said they have been initiating various economizing efforts in the operating budget in recent years, with the largest cut of nearly $6 million being made in the 1976-77 school budget. But these cuts and savings gained from smaller enrollments "are eaten up," Cole said, by state and federally mandated programs, negotiated teacher salary increases and inflation.

Next year's budget proposal, $19.6 million more than the current budget of $267.1 million (a 7.3 per cent increase), is an example of this quandary.

In the budget unveiled yesterday, $4.4 million in saving is projected because of a declining enrollment, relaxed requirements for replacement of school buses, a cut in funds for adult instruction and the elimination of unsuccessful programs or ones for which federal aid will not be continued.

But these savings will be offset by other rising costs, the largest of which is $11.3 million to provide 5.4 per cent salary increases for school employees. Personnell costs account for 87 per cent of the proposed budget.

Another huge increase will be in health insurance payments - up $2.5 million over this year's payment because of a 60 per cent premium increases announced by Blue Cross-Blue Shield, school officials said. The school system has already absorbed a 54 per cent increase in its health insurance payments this year.

Utility and fuel bills will cost $800,000 more next year and complying with state-required special education programs will require an additional expenditure of $250,000, school officials said.

Despite these rising costs, Davis said the budget does not have any funding for new instructional programs. The budget, which Davis said he felt could not sustain "any significant reduction," provides for $19.3 million for debt on construction bonds, $12 million for the school lunch program; $13 million for school construction and $2.6 million for the employee retirement fund as well as $239.7 million for the 1977-78 operating budget.

School finance officials said the county's proposed share of the total budget is $18.7 million more than currently because state aid to Fairfax schools is expected to increase only $1 million next year and federal aid is scheduled to decrease by $6.5 million because of changes in the federal impact aid program for jurisdictions that contain federal installations.

County executive Leonard L. Whorton said he thought the school budget "looked fairly realistic" and that the additional $18.7 million could be "worked into the county's financial plans." He said, however, he didn't know if it could be done without a tax increase.

The county School Board is scheduled to hold public hearings on the budget later this month before adopting it. The county Board of Supervisors eventually will consider and adopt a combined school and county government budget by the end of May.

All the metropolitan school systems are predicting a further decline in student enrollment in the future. In Fairfax county, which may be the fastest-growing area in the next five years, school officials are paradoxically projecting that they will lose 1,800 students each year up to 1982.

Deputy county excutive, Samuel A. Finz, explain that even with an anticipated growth rate of 4 per cent a year, the school population in Fairfax is expected to decline because more single people and families with fewer children will move into the county.

Montgomery County's school planning director, George W. Fisher, gave similar reasons for declining membership in Montgomery schools, which lost 4,670 students this year alone. Fisher said the county's sewer moratorium - which has drastically curtailed home building - is another reason for the loss in student population. He predicts Montgomery's school enrollment will shrink by another 23,000 students between now and 1982.

Finz pointed out, however, that a smaller school population does not mean that new schools won't be needed. "The growth in Fairfax will not be even distributed," he said. Suburban sprawl means that new schools will have to be constructed in booming communities in the western part of the county.

Although the cost of constructing these schools is to be financed by bond sales (if approved by the voters next June) these facilities will require maintenance and staffing whose cots will go into the school system's operating budgets.