When Washington business leaders are asked why the D.C. metropolitan area exploded into a major corporate and professional center over the past 15 years, the Kennedy Center invariably is near the top of the list.

The cultural complex on the Potomac is symbolic to these business people of vitality in the District and its suburbs--nightlife, museums, concerts, restaurants and a broad range of entertainment and leisure pursuits that had not been a notable part of Washington in pre-Kennedy Center days.

For the most part, big government's role in the economy and every industry was probably the main factor behind Washington's expansion in the 1960s and 1970s as a business and professional community.

But the growing cultural amenities here and generally comfortable residential communities were substantial added attractions that lured many outsiders.

Today, many of Washington's cultural organizations are threatened by financial weakness, and Washington business is being asked to help replace some of the funding that has come in previous years from the federal government.

As part of a broad effort to demonstrate what the needs are and why they are important to this community, a study was published last week that provides for the first time information about the economic impact of existing cultural groups in metropolitan Washington.

The Community Foundation of Greater Washington, a public foundation that receives and distributes money from corporations and individuals, completed an 18-month report called "A Cultural Assessment," in collaboration with the Cultural Alliance of Greater Washington and the D.C. Commission on the Arts and Humanities.

Out of an estimated 450 cultural organizations in metropolitan Washington, 342 responded to the Community Foundation's survey, providing the most comprehensive base of data ever gathered on this nonprofit sector.

Most of the organizations have annual operating budgets of less than $100,000 a year. The majority of these smaller groups have no cash reserves or endowments upon which to draw in the event of a shortfall in revenues or a cost overrun. There is no opportunity for deficit spending, one alternative (albeit unpopular) open to the larger organizations, the report noted.

In fact, the smaller groups often "live a catch-as-catch-can existence," not always reflected in financial statements. A small choral group in need of uniforms may get them from members of the chorus, each buying with their own funds, for example.

Overall, the Community Foundation study found cultural organizations in the area add up to a growing but fragile element of the local economy. The arts groups are young, popular and active, but they have been heavily dependent on federal financial help.

Some of the report's key findings include:

* Three-fourths of the organizations surveyed were started in the last 20 years and more than 58 percent were established just in the last decade.

* A small number of large organizations accounted for most of the economic activity--3 percent of the groups surveyed, with annual budgets each over $1 million, accounted for 83 percent of total spending.

* More than 7 million people attended exhibitions, performances and cultural events of the organizations surveyed in fiscal year 1980, the most recent figures available. More than 90 percent of the people involved District-area residents, 8 percent came from other U.S. locations and one percent from overseas. (Not included is the Smithsonian Institution's array of museums and cultural programs, which attracted 21 million visitors in fiscal 1980).

* There were about 12,400 paid employes--1,303 full-time and the balance part-time. In addition, 181 of the organizations reported 9,788 volunteer workers who provided more than 660,000 hours a year of free services.

* Total spending by groups in the survey which had available data was $82.8 million in fiscal 1980; Smithsonian spending in the same year was more than $200 million. Of the survey group, 107 provided data on purchases of goods and services with a total of $10.4 million, 92 percent from Washington-area businesses.

In addition to the overall figures, the Community Foundation study includes a more detailed look at the financial operations of 10 large organizations with budgets of more than $500,000 a year and the biggest economic impact. Included are the National Symphony, Washington Performing Arts Society, Ford's Theatre and the Corcoran Gallery of Art.

The 10 organizations had a combined income of about $31 million, with 45 percent coming from earned income (ticket sales, membership fees, tuition for classes); 28 percent from private sources (gifts from individuals, businesses, foundations, benefit performances); and more than 18 percent from the federal government. Ticket sales alone accounted for the largest revenue source (28 percent of the $31 million), followed by U.S. government aid. n the expense side, about 53 percent of the outlays were for salaries, wages, fringe benefits and other payroll costs; 28 percent was allocated to cultural program activities; 14 percent was administrative costs and 6 percent went to facilities.

Of 5,700 persons employed by these organizations, half were residents of the District. Total salaries, wages and fees for all workers exceeded $14 million a year and at least $580,000 was contributed to the local tax base through arts group payments or through employe withholding.

Looking ahead, 68 percent of the groups surveyed by the Community Foundation said current facilities will not be adequate within three years; a third said increased rents and maintenance fees or lease expirations will cause a relocation.

While financial statements of the smaller groups indicate break-even operations, the survey noted that many have insufficient space, too small a staff for the size of their programs and inadequate funds to make long-range planning or even short-term survival possible.

With major cuts in federal spending, the arts groups will have to find financial support from other sources. And that's the real challenge to all Washingtonians offered in last week's report.

Financial support for the Community Foundation study was provided by the Max and Victoria Dreyfus Foundation, Appleby Foundation, Chesapeake & Potomac Telephone Co., D.C. Commission on Arts and Humanities and the National Endowment for the Arts. Copies of the report are available for $5 and a complete table of findings may be purchased for $25, both from the Community Foundation, 3221 M St. NW, Washington 20007.