Washington — Central bankers of the world, including Paul A. Volcker and his colleagues at the Federal Reserve, have worked out a rough formula for what is needed to keep the international debt burden from collapsing into crisis.
The formula springs from the premise that third-world nations must be able to export more of their own goods if they are to have any hope of repaying their debts to Western banks and governments.
Those debts total at least $600 billion, of which Mexico, Brazil, and Argentina alone owe more than $200 billion. Another $60 billion is owed by Venezuela, Chile, and Peru.
Boiled down, the formula foresees economic recovery among industrial powers, enabling them to buy more goods from debtor lands, plus the lending of fresh billions by Western banks.
''If the economies of the rich nations grow by 1 percent this year,'' said a top central banker in an interview, ''exports from third-world debtors should increase by $5 to $10 billion in 1983.
''This would be coupled with a 7 percent increase in lending to the debtors, '' the banker said, ''or roughly $15 to $20 billion in new loan commitments. If these ideal conditions are met, the situation overall should be manageable.''
''Dangerous, delicate, but manageable'' is the way another senior banker characterized the debt problem. ''Only if developing countries can finance their economic growth (through borrowing) can the debts finally be whittled down.''
The United States emerges as a critical factor in making the formula work:
* The US economy is expected to grow by about 5 percent this year, enough to substantially boost American imports from third-world lands.
Japan also is growing fairly briskly. But Western Europe remains in the economic doldrums, with an overall growth rate of only 0.5 percent predicted for 1983.
* Major US banks, the big lenders to Latin America, must take the lead in new loans.
* A US pledge to up its contribution to the International Monetary Fund by $8 .4 billion will need to be honored by Congress, or other IMF members may renege on their pledges.
What happens to US interest rates this year is of vital concern to bankers - both central and private - striving to keep the international monetary system on course.
Overseas investors, judging by a rush to increase their dollar holdings, seem to be betting that US rates will climb. The dollar is pushing to new highs in value against a range of European currencies.
Two prestigious international bodies - the Bank for International Settlements (BIS) in Switzerland and the Paris-based Organization for Economic Cooperation and Development (OECD) - warn that American interest rates must decline, not rise, to protect the world's fragile recovery.
Both the BIS and the OECD point a finger at the Reagan administration's huge budget deficit as a prime cause of high US interest rates and urge that the deficits be controlled.
This plea is echoed by Fed chairman Volcker, who told Congress July 28 that signs of a clash between public- and private-sector borrowing already are emerging, putting upward pressure on interest rates.
A group of Wall Street experts, said a Fed source, ''almost to a man'' told the Federal Reserve Board that they foresee a borrowing squeeze coming before the 1984 presidential election, not after, as the White House hopes.
High interest rates make debt repayment more expensive for developing countries. Declining rates make it easier for them to borrow to finance economic development.
The formula for managing the debt crisis strikes an average, both for growth among OECD members and for fresh lending to debtors. ''But,'' said a Federal Reserve source, ''not all debtor countries fit the average, so pitfalls remain.''
In Portland, Maine, meanwhile, state governors attending the National Governors' Association warned that yawning budget deficits threaten to choke off the recovery.
The governors cited their earlier appeal for reducing the deficit to 2 percent of the gross national product by 1988. Currently, the deficit is 6 percent of the GNP.