Federal workers and military personnel are due a catch-up-with industry raise this fall that is more than double the 5.5 percent President Carter actually intends to give them.

A just released study by the Bureau of Labor Statistics shows both the cost-of-living and private salaries up much higher than federal pay, which for the second year in a row is scheduled to be limited to a 5.5 percent adjustment this October.

According to the BSL study of private sector pay gains, white collar salaries jumped an average of 7.8 percent between March 1978 and March of this year. The cost-of-living increase during the same 12-month period was 10.2 percent.

Almost identical BLS data is used by federal pay planners to arrive at a recommended "comparability with industry" figure that is proposed to the president by his agents. For pay-fixing purposes the agents are the directors of the Office of Personnel Management, Office of Management and Budget and Secretary of Labor.

But President Carter has intentionally short-circuited the pay process this year. In January, he announced that federal-military pay this year, as it was in 1978, would be limited to a maximum 5.5 percent raise. Carter said it was necessary to fight inflation, and get both labor and management in the private sector to follow his voluntary 7 percent wage-price-increase guidelines.

Last year the president's agents said that a federal pay raise in excess of 8 percent would be needed to bring benchmark federal jobs up to the same pay level as counterpart occupations in industry.

Federal pay experts expect that the actual "comparability" raise due government employes this year will be several points over Carter's 5.5 percent limit. That portion, plus the portion of raises denied civil servants in 1978 must, by law, be paid them some day.

Under the complicated federal pay-fixing system, which the White House is seeking to change, government salaries are supposed to be roughly equivalent with rates paid for similar jobs in industry.

According to the pay plan BLS makes wages surveys and the data is used by the president's agents - in consultation with federal labor unions - to arrive at a "comparability" figure. If the president accepts that figure, the raises automatically go into effect in October. If, however, he recommends a lower alternate amount (as he did in 1978 and will do again this year) he must do so by the end of August.

Unless Congress vetoes the lower figure within 30 days - it did not last year and is unlikely to this year - the lower amount recommended by the president then goes into effect in October.

The federal pay picture is even more complicated this year since Carter announced the amount of the raise before any data was in, and also because there are no federal unions represented on the advisory pay panel. They quit in disgust last year.

"We keep having the party," said one government official of the pay consultation process, "but nobody comes to it except our side." Federal union leaders say that since the president's mind was made up in January, there is little point in dignifying the process by pretending to act as advisers.

Over the next few months federal workers will read and hear a lot about higher amounts due them, and about efforts from the local congressional delegation to get them more money.

The hard political-facts-of-life are that limiting federal pay raises is very popular in most places outside metropolitan Washington, where most adults work for the government. No matter what figures are batted around, it looks like 5.5 percent is the size of the October raise unless the president himself ups the amount. And that ins't in the cards.