Computing the Unemployment Rate
The unemployment rate is the unemployed divided by the labor force. The hard part is knowing who belongs in the denominator.
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What this means
The unemployment rate is a fraction, and the arithmetic is simple. The unemployed go on top. The labor force goes on the bottom. Multiply by 100 to state it as a percentage.
The formula is: unemployment rate equals the number unemployed divided by the size of the labor force.
Almost nobody gets this wrong because of the division. People get it wrong because of the denominator. The bottom of the fraction is the labor force, which means the employed plus the unemployed and nothing else. It is not the population. It is not the number of adults. It is not everyone over a certain age.
So before you can divide, you usually have to build the denominator yourself. You are given the employed and the unemployed separately, and you add them.
Work the April 2020 figures the standard supplies. The number unemployed was 23,090,000 and the number employed was 133,185,000. Add those two to get the labor force: 156,275,000. Now divide 23,090,000 by 156,275,000, which gives about 0.148, or roughly 14.8 percent.
Notice what you did not use. The problem also tells you the number of retirees was 46,000,000, and that figure never entered the calculation. Retirees are not employed and they are not seeking work, so they are not in the labor force, so they belong nowhere in this fraction. Adding them to the denominator would give roughly 11.4 percent, which is wrong. That number is not there to help you. It is there to see whether you know the rule.
Why it matters
Every unemployment headline you will ever read was produced by this exact fraction, and the fraction is only as meaningful as its denominator. Understanding that the bottom is the labor force explains a fact that otherwise looks like a contradiction: the unemployment rate can fall in a month when nobody found a job, because people who stopped searching leave the labor force and shrink both the top and the bottom at once.
It also protects you from a common misreading. An unemployment rate of about 15 percent does not mean 15 percent of the country is out of work. It means roughly 15 out of every 100 people in the labor force are unemployed, and a large share of the population, including everyone under 16, retirees, and full-time students, is not in the labor force at all.
Real-world example
The Bureau of Labor Statistics publishes the employed count, the unemployed count, the labor force total, and the resulting rate every month, all in the same release. Pull the current release and you can rebuild the headline number yourself: add the employed and the unemployed, divide the unemployed by that total, and check your answer against the rate BLS printed. If your figure matches to a tenth of a percentage point, you have the formula right.
Try it
- Write the formula at the top of your page before touching any numbers, and label which quantity goes on top and which goes on the bottom.
- Solve the April 2020 problem, showing four separate steps: list what you were given, build the labor force, divide, convert to a percentage. Round to one decimal place.
- Circle every figure you were given but did not use. Write one sentence explaining why each unused figure does not belong in the calculation.
- Deliberately compute it wrong. Redo the division with the retirees added into the denominator and record that answer too. Then write down how far off it is from your correct answer and in which direction.
- Explain in writing why the wrong answer in step 4 came out lower than the correct one. Your explanation must talk about what happened to the denominator.
- Build your own trap problem. Invent a small imaginary town, give it employed and unemployed counts, and add at least two irrelevant figures such as retirees, children, or full-time students. Solve it yourself first and keep the answer hidden.
- Trade with a partner. Solve their problem and, separately, list which of their figures were distractors. Score two things: the correct rate, and correctly identifying every distractor.
- Look up the most recent national unemployment rate from the Bureau of Labor Statistics along with the employed and unemployed counts from the same release. Recompute the rate yourself and check it against the published figure.
- Answer this in a short paragraph: if 1,000,000 unemployed people gave up searching next month and nothing else changed, what happens to the unemployment rate, and why is that movement misleading?
Teacher note
The retiree figure is the whole point of the source problem. It is a deliberate distractor, and students who do not know the definition of the labor force will use it, because a problem that hands you three numbers feels like it wants all three. Do not warn them in advance. Let them make the error, then use steps 4 and 5 to make it instructive rather than just wrong.
Step 5 is where the understanding actually forms. Students can compute both answers and still not see why the wrong one is lower. Make them articulate it: adding 46,000,000 to the denominator while the numerator stays fixed necessarily shrinks the fraction. That mechanical insight is what makes step 9 tractable, since a shrinking denominator is also the mechanism behind discouraged workers pulling the rate down.
Grade step 7 on distractor identification, not only on the arithmetic. A student who gets the right rate but cannot say which figures were noise got lucky with a problem that had an obvious structure.
Two other things to watch. Students sometimes divide the unemployed by the employed rather than by the labor force, which for these figures produces about 17.3 percent; catch it by requiring the labor force to be written on its own line in step 2. And students will read a rate near 15 percent as "15 percent of Americans have no job," which is a different and much larger claim. Correct it explicitly.
A student has it when they can state, unprompted, that the denominator is the labor force rather than the population, and can name which given figures do not belong in it.
Check yourself
What is the formula for the unemployment rate?
In April 2020 the number unemployed was 23,090,000 and the number employed was 133,185,000. What was the size of the labor force?
Using those same April 2020 figures, what was the unemployment rate, rounded to one decimal place?
The April 2020 problem also states that the number of retirees was 46,000,000. How should that figure be used?
The unemployment rate is the unemployed divided by the labor force, so anyone outside the labor force, including every retiree, never belongs in the denominator.