Fermi estimate - Definition and Overview

A Fermi estimate (or Fermi calculation) is a type of estimation problem that initially appears difficult or impossible due to lack of data, but can be answered (typically to within an order of magnitude of the correct value) by appropriate use of intermediate estimates. These problems are named for the physicist Enrico Fermi, who often posed them to his students.

As an example, the most famous Fermi estimate requires estimating the number of piano tuners in Chicago (or any other large city) from the population of that city. Fermi began by using the population to estimate the number of families, and by estimating the proportion of families that would own a piano he estimated the total number of pianos. By estimating how many pianos one tuner could service in a day, and how many days each tuner would work in a year, he then found the number of tuners necessary to service these pianos.

Many scientists use Fermi estimates to estimate the answer to a problem before turning to more sophisticated methods to calculate a precise answer. This provides a useful check on the results: where the complexity of a precise calculation might obscure a large error, the simplicity of Fermi calculations makes them far less susceptible to such mistakes. (Performing the Fermi calculation first is preferable because the intermediate estimates might otherwise be biased by knowledge of the 'precise' answer.)

Fermi estimates are also useful in approaching problems where the optimal choice of method may depend on the size of the answer. For instance, a Fermi estimate might indicate whether the internal stresses of a structure are low enough that it can be accurately described by linear elasticity.

External links

Two worked examples and 18 sample Fermi questions (http://iws.ccccd.edu/mbrooks/demos/fermi_questions.htm)