There are different estimates of the number of unemployed and the unemployment rate (in percent). This paper explains the differences and adds other categories that might well be described as unemployed. While official unemployment in June 2006 is 4.8%, real unemployment is 12,3%, which includes those who want a job now but are classified as "not in the labor market" and additional jobs needed to keep up with population growth since April 2000 when employment began to decline.

Note that none of this includes the underemployed, which adds considerably to slack in the "labor market."

The official definitions from the BLS web site are given further below, but in brief:

• U-3. the official unemployment rate
• U-4. Adding also "discouraged" workers
• U-5. Adding also other "marginally attached"
• U-6. Adding also "part time for economic reasons" -- they want, but can't find, a full time job
• U-6 + Want Job Now. Adding also those government considers "Not in labor force, but Persons who currently want a job." While there's a certain tortured logic to the BLS definition, I find it stunning that people who say they want a job now, but don't have one, aren't considered part of the labor force.
• U-6 + Want Job Now + Needed to Keep Up w/Pop Growth. Adding also the number of jobs that would be needed to keep up with population growth.

A list of the official definitions and a complete explanation of the equations used to calculate the different values and percentages are included below.
- Official unemployment rate definitions
- Equations to calculate real unemployment

The number of jobs needed to keep up with population growth is shown in the chart below.

Number of jobs needed to keep up with population growth

The different time series for the number of unemployed are shown in the chart below.

Various measures for the number of unemployed

The different time series for the unemployment rates (in percent) for each of these levels is shown in the chart below.

Various measures for the percentage of unemployed

Data sources and Equations

As can be seen below, figuring this out is really complicated. Government has made it so complicated that it actually leads me to think that it's on purpose. The U.S. government does not want to officially admit that there's an effective 20M person (over 12%) slack in the labor force ( 20M / ~160M = ~12%). And this does not include the underemployed.

At this link find
Labor Force Statistics from the Current Population Survey
Table A-1. Employment status of the civilian population by sex and age (Numbers in thousands)

To obtain official data series for:

Civilian noninstitutional population
Civilian labor force
Participation rate
Employed
Employment-population ratio
Unemployed
Unemployment rate
Not in labor force
Persons who currently want a job

For information explaining the meaning of this data see the Issues in Labor Statistics document from the Bureau of Labor Statistics on Labor Supply in a Tight Labor Market (Summary 00-13 June 2000)

Here's an excerpt. It explains (italics in original) that:

Moving beyond the unemployed to look for an additional labor reserve, one can evaluate those who are neither working nor actively looking for work -- that is, not in the labor force. These individuals have varying degrees of interest in taking a job. In 1999, for example, 4.6 million persons outside the labor force were reported to currently want a job. (See chart.) Within this group, there were 1.2 million who were marginally attached to the labor force (including discouraged workers) -- that is, they were available for work and had searched for a job sometime in the year preceding the survey, but were not currently looking for work. The 4.6 million people who indicated that they wanted a job cited a variety of reasons for not currently looking for work. Some reported that they were in school, others had family responsibilities, and some were disheartened about their employment prospects. These and other reasons reflected conditions that may have been preventing their entry into the job market at the time they were being surveyed.

Assuming that all those who indicated they wanted a job could, under different circumstances, enter the job market, there would be 4.6 million persons, in addition to the unemployed, who represented potential labor supply. Together, the sum of unemployed persons and those not in the labor force who want a job has been called the pool of available workers. This unofficial measure is used to gauge changes in the potential labor supply.

Persons not in the labor force, 1999 annual averages

Persons considered not in the labor force, with 1999 annual averages

Definitions of unemployment measures

In Table A-12. Alternative measures of labor underutilization find "Not seasonally adjusted" and "Seasonally adjusted" data series for unemployment measures U-1 through U-6 (in percent). Note that  U-3 is the commonly-cited "official unemployment rate."

Definitions:

U-1 Persons unemployed 15 weeks or longer, as a percent of the civilian labor force

U-2 Job losers and persons who completed temporary jobs, as a percent of the civilian labor force

U-3 Total unemployed, as a percent of the civilian labor force (official unemployment rate)

U-4 Total unemployed plus discouraged workers, as a percent of the civilian labor force plus discouraged workers

U-5 Total unemployed, plus discouraged workers, plus all other marginally attached workers, as a percent of the civilian labor force plus all marginally attached workers

U-6 Total unemployed, plus all marginally attached workers, plus total employed part time for economic reasons, as a percent of the civilian labor force plus all marginally attached workers

NOTE: Marginally attached workers are persons who currently are neither working nor looking for work but indicate that they want and are available for a job and have looked for work sometime in the recent past. Discouraged workers, a subset of the marginally attached, have given a job-market related reason for not currently looking for a job. Persons employed part time for economic reasons are those who want and are available for full-time work but have had to settle for a part-time schedule. For further information, see "BLS introduces new range of alternative unemployment measures," in the October 1995 issue of the Monthly Labor Review.

I define a U-7 and U-8 below.

U-7 includes the extra "Not in labor force, but Persons who currently want a job" that aren't already included in U-6 (the discouraged and other marginally attached that are counted in "Not in labor force, but Persons who currently want a job").

U-8 includes the jobs needed to keep up with population growth.

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Equations for determining unemployment levels from published BLS labor force and unemployment statistics:

One can use the definitions above using algebra to work backwards and find the actual number of persons in the "discouraged," "other marginally attached," and "part time for economic reasons" categories.

Below are the abbreviations and equations:

Abbreviations
UE = Unemployed   ... we know
LF = Labor Force    ... we know
D = Discouraged     ... derive from U-3 and above
OM = Other Marginal  ... derive from U-4 and above
PT = Part time for economic reasons ... derive from U-5 and above

Intermediate abbreviations:
LD = Labor Force + Discouraged
= LF + D
M = Marginal
= Discouraged + Other Marginal
= D + OM
__________

U-3, U-4, U-5, U-6 definitions from
Table A-12. Alternative measures of labor underutilization
__________

U-3 Total unemployed, as a percent of the civilian labor force (official unemployment rate)

U3 = UE / LF
__________

U-4 Total unemployed plus discouraged workers, as a percent of the civilian labor force plus discouraged workers

U4 = (UE + D) / (LF + D)

(D/LF) * (1 - U4) = U4 - U3

D = LF * (U4 - U3) / (1 - U4)
__________

U-5 Total unemployed, plus discouraged workers, plus all other marginally attached workers, as a percent of the civilian labor force plus all marginally attached workers

U5 = (UE + D + OM) / (LF + D + OM)

... divide numerator and denominator by (LF + D)

= [(UE + D) / (LF + D) + OM / (LF + D)] / [(1 + OM / (LF + D)]

... substitute (UE + D) / (LF + D) = U4

= [(U4 + OM / LF + D)] / [1 + OM / (LF + D)]

... substitute LF + D = LD

=  (U4 + OM / LD) / ( 1 + OM / LD)

... multiply both sides by ( 1 + OM / LD)

U5 + U5 * OM / LD = U4 + OM / LD

... rearrange

U5 - U4 = (OM / LD) * (1 - U5)

OM = LD * (U5 - U4) / (1 - U5)
__________

U-6 Total unemployed, plus all marginally attached workers, plus total employed part time for economic reasons, as a percent of the civilian labor force plus all marginally attached workers

U6 = (UE + M + PT) / (LF + M)

PT = U6 * (LF + M) - (UE + M)

__________

Considering extra jobs defined as "Not in labor force, but Persons who currently want a job," define a new U-7 including "Want Job Now" (WJN) ... (note that some of "Want Job Now" are already included in U-6):

U-7 = U-6 + Extra Want Job Now Unemployment
... add the Extra Want Job Now to both the numerator and denominator.

Extra Want Job Now = WJN - D - OM = WJN - M
(marginal = discouraged + other marginal)

U-7 =  (UE + M + PT + (WJN - M)) / (LF + M + (WJN - M))

__________

Considering jobs needed to keep up with population growth from Dec 00 peak define a new U-8 including "Keep Up w/Pop" (KUP):

U-8 = U-6 + Extra Want Job Now + Needed to Keep Up w/Pop Growth.

U-8 =  (UE + M + PT + (WJN - M) + KUP ) / (LF + M + (WJN - M) + KUP)