President Reagan made a powerful plea last week for cuts in federal spending, suggesting in a nationally televised speech that budget deficits and a rising public debt are threats to the nation's economic future.

"The one thing we cannot do is stay on the immoral, dead-end course of deficit spending," he declared.

"Despite your worries and all the warnings, the trend has continued year after year," the president told his audience. "We've had only one balanced budget in the last quarter-century. As a nation, our debt has grown and grown and grown until now it totals $1.7 trillion -- a number so big that it's nearly unimaginable. A single billion is 1,000 millions. A trillion is a million millions."

What Reagan did not spell out in his speech is how much of that debt has been accumulated during his presidency, when spending increases have been slowed substantially except for defense and for interest payments on mounting debt.

When the president took office, the gross federal debt was about $940 billion. Currently it is about $1.7 trillion. Before the end of this year, the debt will have doubled during Reagan's presidency, according to administration estimates,

Or put another way, the debt already has gone up more under Reagan than it did in the 40 years prior to 1981. Even if the figures are adjusted for inflation and changes in the size of the economy, the increase in the debt in the last four years has been spectacular.

In his speech, the president pleaded for support for the compromise budget proposal he struck with the Senate Republican leadership, implying that its passage would rein in the soaring deficits. However, the budget deficits are so large that, even with the proposed spending cuts plus solid economic growth of 4 percent a year and sharply falling interest rates, the debt would continue to increase rapidly.

The federal debt is the sum of all the money owed by the federal government to investors holding securities issued by the Treasury and other government agencies. Some of the debt has been owed for a long time. Some was issued only last week. The deficit is the gap each year between government receipts and expenditures. The debt represents the cumulative effect of past deficits.

By administration estimates, the debt would be approaching $2.5 trillion by the end of Reagan's second term even if everything were to go exactly as planned.

The deficit-reduction plan would cut prospective deficits, but the "tidal wave of debt" still would be mounting.

"Today, our national debt amounts to nearly $8,000 for every man, woman and child in America, and it's increasing by about $1,000 per person each and every year," the president said. "Just to cover the interest on that debt, the federal government will spend $155 billion this year alone. That's more than its entire budget as recently as 1966."

The impact that interest payments have on the budget is remarkable. Between fiscal 1980 and 1984, these payments more than doubled. The president used a gross figure for interest payments. Net interest payments, not counting payments to the government itself, have gone from $52.5 billion in 1980 to $111.1 billion last year and an estimated $130.4 billion this year.

If these net interest payments are removed from the budget, and the remainder of the budget adjusted for inflation, some dramatic trends emerge:

* During the four years of the Carter administration -- 1977 to 1981 -- defense spending rose 10.8 percent. All nondefense spending other than for interest payments rose 10.1 percent.

* During the Reagan years -- 1981 to 1985 -- defense spending has gone up almost 30 percent in real terms, while nondefense outlays, less interest payments, have gone down 1.1 percent. As a result, nondefense spending less interest payments is 1 1/3 times defense spending this year, adjusted for inflation. It was 1 3/4 times defense spending at the beginning of the Reagan administration, again in real terms.

With the additional spending cuts in the compromise budget plan, by the end of Reagan's second term, the real level of defense outlays will be only slightly smaller than total spending for everything else except interest.

The budget compromise, which the administration is calling the "Taxpayers' Protection Plan," includes somewhat smaller defense increases than had been requested in the past. But most of the plan's reductions come from elsewhere in the budget, which in the aggregate and adjusted for inflation has fallen slightly over the last four years. These nondefense areas would bear the brunt of spending cuts in the compromise.

With the cuts, the plan will bring us "within reach of a balanced budget by 1990," he said. "And it will do this not by raising your taxes, but by reversing 20 years of overspending."

Back in 1977, the gross federal debt was 38.1 percent of the gross national product. By 1981, the ratio had dropped to 34.8 percent.

If the president's plea for spending cuts is successful and everything else goes exactly right, in 1990 -- the year that the budget approaches balance -- the debt-to-GNP ratio will be about 47 percent, just about where it is this year. The total debt will be close to $2.7 trillion -- in Reagan's words, a million million dollars more than it is now.