Fermi problems typically involve making justified guesses about quantities and their variance or lower and upper bounds.
The estimation technique is named after physicist Enrico Fermi as he was known for his ability to make good approximate calculations with little or no actual data.
An example is Enrico Fermi's estimate of the strength of the atomic bomb that detonated at the Trinity test, based on the distance traveled by pieces of paper he dropped from his hand during the blast.
That is, if there is no consistent bias, a Fermi calculation that involves the multiplication of several estimated factors (such as the number of piano tuners in Chicago) will probably be more accurate than might be first supposed.
While the estimate is almost certainly incorrect, it is also a simple calculation that allows for easy error checking, and to find faulty assumptions if the figure produced is far beyond what we might reasonably expect.
Without a reasonable frame of reference to work from it is seldom clear if a result is acceptably precise or is many degrees of magnitude (tens or hundreds of times) too big or too small.
If their initial estimate told them there should be a hundred or so, but the precise answer tells them there are many thousands, then they know they need to find out why there is this divergence from the expected result.
First looking for errors, then for factors the estimation did not take account of – does Chicago have a number of music schools or other places with a disproportionately high ratio of pianos to people?
Fermi estimates are also useful in approaching problems where the optimal choice of calculation method depends on the expected size of the answer.
[citation needed] Although Fermi calculations are often not accurate, as there may be many problems with their assumptions, this sort of analysis does inform one what to look for to get a better answer.
It also gives a rough estimate that may be good enough for some purposes: if a person wants to start a store in Chicago that sells piano tuning equipment, and calculates that they need 10,000 potential customers to stay in business, they can reasonably assume that the above estimate is far enough below 10,000 that they should consider a different business plan (and, with a little more work, they could compute a rough upper bound on the number of piano tuners by considering the most extreme reasonable values that could appear in each of their assumptions).