Fermi problem

In physics or engineering education, a Fermi problem, Fermi quiz, Fermi question, Fermi estimate, or order estimation is an estimation problem designed to teach dimensional analysis, approximation, and such a problem is usually a back-of-the-envelope calculation. 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. Fermi problems typically involve making justified guesses about quantities and their variance or lower and upper bounds.

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. Fermi's estimate of 10 kilotons of TNT was remarkably close to the now-accepted value of around 20 kilotons.

An example problem, of a type generally attributed to Fermi, is "How many piano tuners are there in Chicago?" A typical solution to this problem involves multiplying a series of estimates that yield the correct answer if the estimates are correct. For example, we might make the following assumptions:

From these assumptions, we can compute that the number of piano tunings in a single year in Chicago is

We can similarly calculate that the average piano tuner performs

Dividing gives

The actual number of piano tuners in Chicago is about 290.

A famous example of a Fermi-problem-like estimate is the Drake equation, which seeks to estimate the number of intelligent civilizations in the galaxy. The basic question of why, if there were a significant number of such civilizations, ours has never encountered any others is called the Fermi paradox.

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