College financial officials this week unveiled estimates of the cost of a Harvard education next year, and they were unexpectedly gloomy: 1982-83 tuition, room and board fees will total between $11,800 and $12,120.

The increase, of between 12 and 15 per cent, will make next year the third straight in which total student costs rose at double-digit rates, and administrators say no end to that trend is likely unless the nation's inflation rate declines dramatically.

If the Corporation decides to raise total costs at a rate higher than last year's 14.9-per-cent clip, the rate of increase would be the highest in decades and probably the highest in college history.

Though the Corporation will not determine precise figures until early winter, Dean Rosovsky predicted this week costs will rise "at least" as fast as last year's. Under that scenario, tuition would jump from today's $10,540 to $12,110.

Perhaps more significantly, officials said, a leap of that magnitude might top the annual rise in family disposable income for the first time in more than a decade.

In the past, the College has successfully kept increases in tuition, room and board combined no higher than national rates of growth--an effort not to price families out of the market for a Harvard education.

But that policy has put the Faculty in what Rosovsky this week called "a very bad economic squeeze" and has, in part, forced the Faculty to raise professors' and staff members' salaries at rates considerably slower than inflation. Since 1970, professors' salaries have lost 15 per cent in real terms.

A decision to shore up Faculty salaries this summer by boosting wages faster than inflation put particular financial pressure on the Faculty budget. The salary hike has effectively nullified gains stemming from recent drops of several points in the rate of inflation and small drops in the rate of increase of the Faculty's energy costs.

Despite the pressure on tuition caused by raising salaries, financial officers stressed that the increases were necessary because of declines in the Faculty's salary levels relative to some other colleges.

"If Harvard did not have a terrific Faculty, it would not be Harvard," Melissa D. Gerrity, associate dean of the Faculty for financial affairs, said.

The need to hike salaries as fast as the rate of inflation while not raising tuition more than inflation has put the Faculty in a touchy financial situation.

Accordingly, Rosovsky, in his annual budget message released this week, calls for careful management to keep the Faculty financially sound over the next decade.

But several problems seem certain to arise. Sharp drops in federal student aid have forced Harvard to raise dramatically expenditures on financial assistance to students; the Faculty may also have to compensate for federal cuts in research grants, particularly to science professors.

Energy, too, will remain a problem, particularly with recently announced price hikes by the Organization of Petroleum Exporting Countries. The Faculty's conservation programs have helped keep the rate of increase of energy costs to a manageable 20 to 25 per cent annually over the last several years, but officials say the potential for new conservation may not be great enough to keep rates of increase at those levels over the long term. Nevertheless, the Faculty's 1981-82 budget assumes no increases in energy expenses over 1980-81.