American motorists will wind up paying more than $9 billion extra in gasoline profits to the oil industry by the end of 1980 as a result of a miscalculation five months ago by the Carter administration, government and oil industry records show.

This financial bonanza for the oil companies can all be traced to the so-called "Tilt Rule," which the U.S. Department of Energy adopted March 1.

Under a complicated formula, the rule allows oil companies to make an additional profit on gasoline - beyond actual crude oil cost increases and operating costs - in recognition that gasoline costs more to produce than other crude oil derivatives.

The idea behind the rule was that the extra profit would act as an incentive to oil companies to build more refineries and thus head off future gasoline shortages.

The Carter administration predicted at the time that the rule would cost motorists an extra 1.6 cents a gallon at the pump in 1979 and another 1.8 cents a gallon in 1980. The rule was supposed to mean a "maximum" of $3.7 billion in added profits for the oil industry.

Instead, when the rule went into effect on March 1, most oil companies took advantage of it to raise their prices an immediate 4 to 6 cents a gallon, according to a survey of major oil companies and interviews with government officials.

The effect of those price increases will balloon the price tag of Tilt up to $12.9 billion by the end of next year.

The second ranking regulatory official in the Energy Department acknowledged in a recent interview that the Carter administration forecast that the Tilt Rule would add 1.6 cents to gasoline prices in 1979 was substantially off base.

That estimate, said Douglas G. Robinson, "was clearly not a valid number for this year."

And there are clear indications that the department knew its projections were faulty when it rushed the Tilt Rule into effect without the usual 30-day waiting period set aside for public comments.

"It is fair to say that we had some indication at that time...and the decision makers were aware of that at the time, but that did not dissuade them from going ahead," said Robinson.

The kicker, industry officials said, is that the financial bonus to the oil industry may yield no new refineries.

Moreover, in a move widely questioned within the Energy Department itself, the Tilt Rule was made retroactive to Jan. 1, an act that was worth additional hundreds of millions of dollars to the oil industry.

Robinson, who wrote the Tilt Rule, acknowledged that there was "absolutely no justification" for making it retroactive.

For a single company, Texaco Inc., the retroactive benefits alone meant $48.9 million in additional profits, according to an internal company document.

The higher profits for oil companies under the Tilt Rule were in fact foreseeable from the outset, but the administration failed to tell the public that a gasoline shortage and rising crude oil prices - already apparent before March - would allow the oil industry to collect billions more than had been predicted.

By far exceeding its predicted generosity, the Tilt Rule has highlighted another paradox of Carter administration energy policy:

In spite of its get-tough-with-the-oil lobby rhetoric and its attack on windfall oil profits, the administration has allowed the oil industry to recover billions of dollars in revenues that would have been lost under the price-control system that existed at the first of the year.

Together with other forms of profit-taking made possible by the Energy Department's pricing regulations, the increase in profits from the Tilt Rule explains why the price of gasoline has gone up much faster than crude oil price increases from the Organization of Petroleum Exporting Countries (OPEC) would appear to justify.

While the most current survey of more than 17,000 service stations shows prices at the pump up a total of 26.9 cents since the first of the year, only 14 cents of that increase can be directly traced to crude oil price increases, federal energy officials say.

A look at one company's experience after the Tilt Rule went into effect helps explain the difference between those two figures.

Between January and July, Texaco raised its wholesale gasoline prices 19 to 20 cents, depending on the area of the country.

A spokesman for Texaco, the third largest U.S. oil company, said that it would be "impossible to quantify" how the Tilt Rule has affected Texaco's revenues this year.

But confidential company records for the first five months of 1979 show the following:

By the end of May, Texaco had raised its wholesale gasoline prices a total of 11 cents and had experienced actual crude oil cost increases of about 4 cents.

In other words, only 36 percent of Texaco's wholesale gasoline price increases was a direct result of crude oil price increases.

According to the records, the rest of Texaco's price increases during those five months included:

A 4.5-cent-a-gallon increase due to the Tilt Rule, which brought Texaco $55 million in additional profits during March and April.

Another fraction-of-a-cent increase beginning in May as Texaco began to collect the $48.9 million in profits from the retroactive portion of the Tilt Rule.

The central justification for the Tilt Rule was that it was "critically important to bringing on sufficient gasoline supplies in 1980," according to Robinson.

"The summer of 1981 would be a complete disaster in this country - it may be anyway - but we wouldn't have helped it any" without Tilt, he added.

"At some point, this country has got to start investing in the future," Robinson said. "In our judgment, the Tilt Rule is two years overdue...(and) if it was done in 1976, it wouldn't have caused a public whisper."

However, Robinson acknowledged that there was "no real study" to determine precisely the need for additional oil refining capacity and the cost of constructing it.

Instead, he said, energy officials surveyed the industry "to see what they were doing" and determined that the oil companies were not investing in new refineries.

However, the presumption that the benefits of the Tilt Rule will actually increase gasoline supplies in the future is discounted by the industry itself.

"Mere manipulation of the present regulations will not contribute much towards improving the investment climate," wrote the planning manager of Mobil Oil Corp. in a Feb. 14 letter to energy officials.

"If the Tilt amendment is to accomplish the announced goal of providing an incentive to create additional domestic (refining) capacity, it must go beyond mere cost recovery," argued Standard Oil of Ohio's D. O. Maxwell in a Jan. 12 letter.

Federal energy officials did not attempt to secure any pledges from the oil industry to build additional refining capacity in return for the extra profits provided by Tilt.

Kitty Shirmer, the White House aide who reviewed the Energy Department's Tilt proposal, said it was "doubtful" that the administration could have legally secured such a pledge.

The technical director of the National Petroleum Refiners Association, Herbert Bruch, said he does not think Tilt will provide the desired incentive to invest in new refineries.

"It's a nice thing we have...but the real problem is that we've got a crude shortage and this is going to dictate the supply of gasoline," Bruch said.

He said that demand for gasoline grows at about 2 percent a year and that with new conservation and efficiency standards for automobiles, the government and industry have been predicting that consumer demand will reach a plateau by 1981.

Together with surplus oil refining capacity in European countries, Bruch said the oil industry is more concerned with having too much gasoline production rather than not enough.

Even the Energy Department's Robinson acknowledged, "It's not really a question that the oil companies need price relief of that they need more money laying around to invest in gasoline capacity." However, he added, the price control system must include a "rational system of apportioning the costs of refining.

Otherwise, Robinson said, there would be greater incentives for oil companies to invest in "department stores, circuses and crude oil capacity," referring to Mobil's purchase of Montgomery Ward & Co. and Gulf Oil Corp.'s reported interest in Ringling Brothers - Barnum & Bailey.

Regardless of its economic impact, the oil companies argue that the Tilt Rule is not something new. Rather, they argue, it eliminates an imbalance in gasoline pricing that began in June 1976, when the government decontrolled home heating oil, diesel fuel and other products that half of a barrel of crude oil yields.

Prior to 1976, oil companies were able to apply refining costs more heavily to gasoline in recognition that gasoline production costs more money.

However, when the fuel oil portion of the barrel was decontrolled, federal energy officials prohibited the oil companies from applying any of the refining costs of the decontrolled products to gasoline as they had in the past.

As a result, refining costs were distributed equally along the product line - not recognizing that gasoline carried a greater refining expense. Oil company officials argue that from that point on, gasoline production was subsidized by other oil products.

"Adoption of the Tilt amendment would do nothing more than correct this deficiency in the regulations," argued Shell Oil Company's G. G. Carnahan in a Jan. 11 letter.

Explaining the Tilt Rule in congressional testimony last spring, the Energy Department's top regulatory official, David J. Bardin, said Tilt was a matter of fairness to the oil companies.

Tilt is based on the premise that since gasoline is more expensive to refine, the industry should be allowed to recover proportionately greater refining costs and profits on gasoline.

Responding to one congressional questioner, who raised the specter of an "inflationary shock wave" resulting from the Tilt Rule, Bardin replied that the Carter administration cannot be "unfair to rich refiners."

"This government must be fair to the rich as well as to the poor, to the productive, as well as to the nonproductive," Bardin said.

Making a new federal regulation retroactive is usually one of the most abhorent government acts to private industry.

However, in the case of the Tilt Rule, most of the major oil companies enthusiastically urged the Energy Department to allow them to collect profits as if the Tilt Rule had been in effect Dec. 1 instead of March 1.

The Energy Department's initial projection was that the retroactive portion of the fule would cost consumers more than $760 million as a one-time cost in 1979.

From the comments submitted by the oil companies while the rule was being considered, Robinson said he concluded that the industry's basic justification was: "We would like some more money, so why don't you give it to us?"

Why then, did the department make the rule retroactive?

Said Robinson: "Why don't you ask my boss?"

Robinson's boss, Bardin, could not be reached for comment.

The Energy Department's special counsel, Paul L. Bloom, who is charged with securing billions of dollars of refunds from the oil industry for price overcharging during the 1973-74 oil shortage, reportedly was furious over the retroactive decision, and ever since refers to it as "Bardin's gift" to the oil companies.

Even the oil industry was not unanimously in favor of pushing back the effective date of the rule.

"We believe that retroactive imposition of regulatory changes is never proper, and do not support retroactive implementation of this proposal," said Standard Oil of Ohio's Maxwell.

But fighting for the opposite course was Texaco's William K. Tell Jr., whose justifications were:

The fule was long overdue.

The Energy Department had first said the rule would be effective Dec. 1, 1978.

And, finally, "No one was relying on a continuation of the existing rule beyond Dec. 1."

Ultimately, Bardin decided on a Jan. 1 retroactive date instead of Dec. 1.

Looking back on all of this, Robinson defends the Energy Department's projections by saying that when they were completed, "We were not in a tight supply market," and to those who understood how the rule worked (see related story) it was apparent that a general shortage of gasoline and rising crude costs would allow the oil companies to collect substantially greater profits.

He also says he was not surprised by the magnitude of those added profits: "At a time like this, you'd expect everybody to get all they could for everything," he said.

As for the 4 to 6 cents that American motorists already are paying because of the Tilt Rule, Robinson was philosophical:

Given that the price of gasoline is more than $30 billion more expensive on an annual basis now that at the first of the year, he says, the $5 billion or $6 billion that can be attributed to Tilt in 1979 "is practically lost in the noise of what is happening now." CAPTION: Picture, DOUGLAS G. of Tilt Rule