Fairfax County Executive Leonard Whorton yesterday proposed a $502.4 million county government budget for 1977-78 that eases many of the austerity measures imposed last year, but requires no tax rate increases.

County officials said, however, that even if the Board of Supervisors does not raise tax rates, most Fairfax real estate owners will be receiving higher tax bills this year - the result of the continuing, though slower, appreciation in value of houses and other properties in the county.

Whorton proposed "limited but important improvements" in services and programs, including adding 18 paramedical emergency workers and 23 police officers and resuming various public works projects halted last year.

The improvements, while they affect only a small part of the half-billion-dollar-plus budget, are nonetheless in sharp contrast to last year's virtual no-growth budget.

The proposed $502.4 million spending figure is down from $540.5 million in the current fiscal year ending June 30. But the current year's budget is abnormally high because it includes cost of many construction projects, which are paid by bonds or, in the case of sewage-treatment plants, largely through federal aid.

Under Whorton's budget, spending for county government agencies and construction would be $213.4 million down from $272.5 million this year, primarily because of the absence of several large sewer projects. Expenditures for the county school system would be $289 million, 57.5 per cent of the total the largest single item.

Spending for the day-to-day operations of the county government, including the school system, would increase from $282.7 million to $315.9 million, an 11.7 per cent increase. Other expenditures - such as for sewers, construction of new county facilities, interest on debts and fee-supported services - make up the balance of the $502.4 million package.

The proposed spending for schools, up from $268 million this year, is the total approved by the county school board. Whorton was required by state law to forward that proposed amount to the supervisors, who can cut, increase or accept the amount. Last year the supervisors trimmed $3.5 million.

If past budget deliberations are a guide, a number of interest groups will charge that Whorton has proposed too much, or too little, spending. Homeowner groups are likely to ask for a tax decrease to offset rising assessments.

The supervisors will have the last word on the budget, making their decision after hearings in April where Fairfax residents will have a chance to express their views.

The county expects a 14.4 per cent increase in county real estate tax revenues, largely because of a state law requiring that all properties be assessed annually. That means that the tax assessors's net - actually a new computer system - will reach every property owner this year. Up to last year, under cyclical assessments, about half the county's homeowners escaped annual reassessments.

The state law also brings a new formula for computing taxes. The tax rate this year will based on 100 per cent of fair market value not 40 per cent as in the past. With the higher assessment a compensating decrease will come in the tax rate.

The old rate of $4.35 per $100 of assessed valuation converts to $1.74. But the tax bill is the same using either formula.

Because houses appreciate differently, increases in individual tax bills will vary. Some houses, according to the computer-assisted assessors, will appreciate 5 per cent, others 10 per cent and some - perhaps older dwellings in declining neighborhoods - will not go up in value or may even decrease.

The 1976 tax on a house value at last year's median Fairfax price of $62,600 was $1,087.50. If the house's value increases by 10 per cent, the bill this year would be $1,196.25.

Whorton's budget - his first as county executive - proposed no dramatic shifts in expenditures. Nor did it contain a message as grim as the one president last year by then-Acting County Executive J. Hamilton Lambert, who proposed a 26 per cent increase in the real estate tax rate - eventually halved by the supervisors - and deep cost cutting, much of it adopted.

Whorton proposed:

"The budget is not as austere as it had to be in past years by any stretch of the imagination," Whorton said. "I would call it a "practical budget."

Restoration of the sidewalk and trails construction program, at a cost of $609,000.

Staffing for four "mobile intensive care units" in Fire and Rescue Services to provide quick treatment for heart-attack victims and to meet other emergencies, at a cost of $529,000.

Addition of 39 positions to meet increased staffing needs at the new adult detention facility, which will open in September. The cost would be $700,000.

Addition of 522 units of limited-income housing, at a cost of $291,513.