The 50th presidential inauguration, the four-day celebration that was plagued by frigid weather and called-off events, cost $9.5 million and came out in the black -- even though officials refunded about $900,000 of the $1.2 million collected for tickets to the canceled inaugural parade, officials announced yesterday.

The festivities, which included fireworks displays and nine elaborate balls to celebrate President Reagan's Jan. 21 swearing-in, came in slightly under the projected budget and far below the record-breaking $16.3 million price tag of Reagan's first inauguration in 1981.

However, the District, which received a federal appropriation for its role in the celebration, spent slightly more than the $2.3 million allocated, according to Joseph P. Yeldell, director of D.C.'s Office of Emergency Preparedness. The cost of the presidential parade reviewing stand -- which was built but never used when the parade was canceled -- accounts for most of the excess, he said.

The District receives public funds to pay for police protection and other services required for the traditional four-day event, but a special presidential inaugural committee raises funds through ticket and souvenir sales to pay for the celebration itself.

That committee owes the black-ink outcome to the sale of tickets to the balls and to a sold-out presidential gala produced by Frank Sinatra and televised on ABC-TV, according to a spokesman. In particular, the Republican faithful gobbled up 750 special boxes at the balls that sold for $2,500 each, he said. That alone came to more than $1.8 million in sales.

Others purchased 62 boxes for $12,000 each at the presidential gala at the Washington Convention Center to see entertainers, including Sinatra, Tom Selleck and Rich Little, perform for the president and the First Lady on Jan 19. Those sales and other boxes that went for $6,000 at a similar vice presidential gala on Jan. 18 brought in more than $1.1 million.

Private firms that lent the committee about $8 million for operations will be repaid next week, inaugural spokesman Tucker Eskew said.

In addition, the committee raised about $900,000 from private and corporate donations for the free public events. Only one, a patriotic pageant that ended with a bang of fireworks on the Mall, survived the bitter cold and drew thousands to the opening of what was to be four days of pageantry.

"We promised to offer the American people high-quality events which could be enjoyed by everyone," said Michael K. Deaver, the White House deputy chief of staff who was general chairman of the inaugural committee. "We were pleased to be able to do so, particularly at a cost which was lower than our expectations."

Planners have been particularly sensitive to the cost factor after Reagan's 1981 Hollywood-style inaugural extravaganza made history with its price tag and its imperial trappings, particularly when compared to President Jimmy Carter's self-styled "Y'all come, people's celebration" in 1977.

Carter's weeklong celebration, where the highest-priced ticket went for $25, took in about $4.5 million in receipts, according to inaugural archivist Jerry Wallace.

Yesterday, Eskew said that when inflation is taken into account, Reagan's 1985 inauguration cost only about 20 percent more than "Carter's bare-bones celebration."

"We got a lot bigger bang for just a few more bucks," he said.

Eskew said the figures are not final because the committee will offer parade ticket refunds through the end of this week. Sales of inaugural memorabilia, an operation that has "about broken even," will continue by mail through March 1, he said.

The bulk of the District's expenditures went for police protection during the inaugural weekend. But when the parade was canceled, the city saved about $120,000 in overtime expense that had been projected, Yeldell said.

The cost of the presidential parade reviewing stand, which was constructed with bullet-proof glass and built to Secret Service specifications, exceeded the approximately $675,000 projected, Yeldell said. That, he believed, will account for the excess expenditures when final figures come in. But he said D.C. will be able to recoup the money by seeking a supplemental appropriation from Congress.