Patients in the Washington area paid an average of $416 a day for hospital care last year--a record for the area--as the price of new equipment, increased labor costs and cuts in federal health programs raised costs by 14 percent.

A study of area hospital costs, released by Blue Cross, shows that costs rose 18.9 percent in Northern Virginia, 13.3 percent in Washington and 9.2 percent in Prince George's and Montgomery counties in 1982.

Nationally, hospital costs rose 17 percent last year, far exceeding the 3.9 percent increase in the Consumer Price Index.

Hospital costs, as defined in the survey, include room and board, medicine, nursing care and use of operating rooms--essentially, the hospital's overhead. Thirty-five area hospitals are covered in the survey.

The area hospitals' average costs per patient per day were $472 in the District, $372 in Northern Virginia and $314 in the Maryland suburbs. The costs do not include fees for doctors' services, nor do they include the hospitals' expenses for bad debts, hospital growth and other losses.

Federal officials in the last several administrations have tried without success to slow the increase in health care costs. The local study shows some encouraging signs, however, in Maryland's efforts to hold down costs.

The more modest increases in the Maryland suburbs, an average of $22 a day, are attributable to a nine-year-old commission that regulates hospital costs, health planners said.

"Over the years since that commission came into being, that law has saved Marylanders close to $300 million," said Rick Wade, a spokesman for the Maryland Hospital Association, adding that the figure represents the difference between Maryland's hospital cost increases and the national average.

The Maryland suburbs also recorded the shortest average length of stay, with patients staying an average of 7.1 days, compared to 9.4 days in the District and 7.3 days in Northern Virginia.

"The key factor in the increases is the new technology that hospitals need to keep up," said John Ashby, assistant executive director of the Washington Hospital Association. "We do feel the increases are trending downward and that we've made some improvement. It may well be a single-digit increase next year."

Washington's hospitals are more costly, Ashby explained, because of the large number of hospitals providing more sophisticated treatment than several of the suburban hospitals. Further, Washington has a greater number of elderly and poor residents who require more health care, he said.

"The nature of the population we're treating is costly," Ashby said. "Infant mortality is high. High unemployment tends to create health problems."

Historically, labor costs account for about 70 percent of hospitals' expenses. At Suburban Hospital in Bethesda, costs jumped in 1982 because it hired extra nurses, improved staff pay for nights and weekends and began a $1 million renovation of an out-patient surgery unit, said assistant administrator Lynn Frank. Its daily charges currently are $320 a day.

At Washington Hospital Center, a 1982 contract that included an 8 percent raise for most nurses, clerical workers and technicians accounted for the hospital's largest increase, said spokeswoman Stephanie McNeill. The burn unit and Med-Star emergency center also recorded a drop in patient volume, which reduced income as costly professionals must remain in the units 24 hours daily regardless, she added.

Room rates at Fairfax Hospital increased last July from $165 to $170, in part to make up federal budget cuts in Medicare and Medicaid reimbursements, said Ann Donahue, director of patient accounts. "Medicare and Medicaid falls long short of covering the costs," she said.

The study also showed that fewer patients entered area hospitals last year, as occupancy rates dropped from 81.1 percent to 79.5 percent.