Enrico Fermi designed the first nuclear reactor to achieve a fission chain reaction.  As a professor at the University of Chicago, Fermi would challenge his students to solve problems that seemed impossible due to lack of given information.  Fermi wanted his students to develop their abilities to make assumptions and estimations and work out rough solutions on the back of an old envelope rather than making detailed (with calculators in your case) calculations.  The typical Fermi problem was to determine the number of piano tuners in Chicago given only the population of the city




Fermi’s solution:

Given Chicago has a population of about 3 million people (in the 1940’s).
Assume that the average family has four members so that the number of families in Chicago must be about 750,000.
Assume one out of five families owns a piano, there will be 150,000 pianos in Chicago.
If the average piano tuner worked 5 days a week tuning 4 pianos each day and had a two week vacation during the summer….
In one year (50 weeks) he would tune 1,000 pianos.  Therefore there must be about 150 piano tuners in Chicago.


This method is not guaranteed correct but it is a valid first estimate that might be off by no more than a factor of 2 or 3 but will definitely not inaccurate by an order of magnitude (we should not expect 15 piano tuners, or 1,500 piano tuners). Notice how many assumptions were made to come up with the answer.


Estimation Strategies


Don’t make numbers more precise than necessary


Guess numbers that you don’t know


Make complicated geometry simple 


Extrapolate from what you do know




When estimating, keep things as simple as possible.  You will use estimate in your lab work, but most often estimation can be used to see if a calculated answer is reasonable (in other words you did not make a calculation error).


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An amusing video showing how estimating can be used to solve improbable problems related to the Boston Marathon



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