To reach his target of reducing the unemployment rate to 6.5 per cent by the end of the year, President Carter will have to hit his growth target of 6 per cent, and may have to exceed it, according to a new set of calculations by the Bureau of Labor Statistics.

Carter's success in reaching that rate will depend heavily on how many Americans start looking for jobs, that is, join the labor force. Former President Ford's record on unemployment, looked bad even though nearly 3 million jobs were created last year because 2.8 million people joined the labor force between December 1975 and December 1976. That was hundreds of thousands more than most analysts expected at the start of last year.

The unemployment rate is difficult to use as a gauge of economic recovery because the way it is defined makes it very sensitive to changes in the numbers of Americans seeking work. The unemployment rate is defined as the percentage of the work force actively seeking work but unable to find it. The labor force itself is, by definition, the sum of those unemployed and those who have jobs.

In testimony before the Joint Economic Committee recently, Commissioner of Labor Statistics Julius Shiskin presented a series of tables which show in a shorthand manner how much real economic growth would be needed to reach a target reduction in the unemployment rate and how many jobs would have to be created to reach a similar reduction.

If the labor force grows by 2 million persons this year, there will have to be 1.8 million more jobs in the economy this year just to keep the unemployment rate level. Shiskin's tables deal in year-to-year averages. While there were nearly 2.8 million more people in the labor force at the end of 1976 than at the end of 1975, the average number of pesons in the labor force in 1976 was 2.2 million more than the average number in 1975.

If there were 87 million persons with jobs in January and 89 million in December and it is assumed that the number of employed grows steadily each month), the average number of employed would be about 88 million for the year.

The unemployment rate averaged 7.7 per cent last year and was 7.8 per cent in December. To get the average rate down to 6.7 per cent this year, economic growth will have to average 5.6 per cent to generate the 2.8 million jobs needed to reduce unemployment by 1 percentage point, according to Shiskin's calculations. Economic growth (as measured by the so-called real gross national product) was 6.2 per cent in 1975, with most it coming early in the year.

Shiskin acknowledges that his calculations are rough ones and make many assumptions. He bases his calculations on increases in productivity, or output per hour worked, of 3 per cent a year. If productivity grows at a slower rate, say 2.5 per cent, then the economic growth rate needed to create 2.8 million jobs falls to from 5.6 to 5.2 per cent. However, many economists think that productivity will rise fairly rapidly in 1977. That would mean industry could achieve a growth rate of 5.6 per cent without employing all of the 2.8 million people Shiskin's table assumes.

Similarly, the growth of the labor force will vary depending on what industries pick up employment this year.

Shiskin said that the rapid growth in the labor force last year "was facilitated by strong employment gains in the service and trade industries, which encouraged the entrance of large numbers of women into the labor force." If the employment growth occurs in manufacturing and construction this year - where there are large numbers of laid-off workers - the labor force growth would be smaller.

Nonetheless, he noted, growth in the service and trade industries is a long-term trend, not a phenomenon unique to 1976.