Today's employment numbers for February illustrate that while mathematically simple, the relationship between employment, unemployment, and the labor force participation rate is complicated.

One might expect that we would have seen a drop in the unemployment rate in February, given the addition of an estimated 227,000 payroll jobs for the month (see the U.S. Bureau of Labor Statistics' Employment Situation for February 2012). However, the share of the working-age population in the labor force (or, rather, the labor force participation rate, LFPR) is estimated to have increased from 63.7 percent in January to 63.9 percent in February. A 0.2 percentage point increase in the LFPR is not unprecedented, but after a year of flat and declining labor force participation, it's notable. There are a lot of reasons why the supply of labor, as represented by the LFPR, rises and falls over time. In the short run, a decision of someone to enter (or re-enter) the labor force could be driven by a reassessment of job prospects. This sort of situation is why the LFPR might rise as an economy improves from a very weak position.

While not its primary purpose, the Federal Reserve Bank of Atlanta's Jobs Calculator, which was introduced last week, can help figure out roughly what the unemployment rate would have been if the LFPR had remained at its January level of 63.7 percent.

From the Jobs Calculator web page, first set the number of months to one. Then set the labor force participation rate to 63.7 percent. Next, adjust the unemployment rate until the average monthly change in payroll employment gets close to 227,000. (For example, an unemployment rate of 7.9 percent results in an estimated change in employment of 250,743, using data from the U.S. Bureau of Labor Statistics's Current Employment Survey. This calculation necessarily assumes that people enter and leave the labor force from unemployment and is only approximate because it's using February data.)

So, if the LFPR had remained at the 63.7 percent it was in January, the unemployment rate would have been roughly 8 percent in February.

Look for enhancements to the Jobs Calculator in the coming months that will make this sort of calculation more straightforward.

By Julie Hotchkiss, a research economist and policy adviser in the Atlanta Fed's research department