How many piano tuners are there in Chicago?

oxford 2011 - the first 014 It seems a simple question, but if you have no internet, it might become very hard to answer it.  This kind of question is known as Fermi Problem, because the famous physicist used to enjoy this kind of game. A Fermi Problem is a way to estimate a certain quantity, with a good approximation,  without using any type of databases.

You can see an example of Fermi Problem in the following reasoning, taken from Wikipedia (

  1. There are approximately 5,000,000 people living in Chicago.
  2. On average, there are two persons in each household in Chicago.
  3. Roughly one household in twenty has a piano that is tuned regularly.
  4. Pianos that are tuned regularly are tuned on average about once per year.
  5. It takes a piano tuner about two hours to tune a piano, including travel time.
  6. Each piano tuner works eight hours in a day, five days in a week, and 50 weeks in a year.

From these assumptions, we can compute that the number of piano tunings in a single year in Chicago is (5,000,000 persons in Chicago) / (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 125,000 piano tunings per year in Chicago.

We can similarly calculate that the average piano tuner performs (50 weeks/year)×(5 days/week)×(8 hours/day)/(2 hours to tune a piano) = 1000 piano tunings per year per piano tuner. And then, dividing gives (125,000 piano tunings per year in Chicago) / (1000 piano tunings per year per piano tuner) = 125 piano tuners in Chicago.

Apart from piano tuners, this kind of reasoning could help us to answer scientific questions too. For example, in 1945 Fermi was able to estimate  the strenght of the atomic bomb detonated at the trinity nuclear test in New Mexico, based on the distance made by pieces of paper dropped from his hand during the test.

But maybe you are asking yourself the reason why I am interested in this kind of estimations. Well, that is because my teacher has given me a special homework last week: I have to estimate in how many places are there in Trieste, people could drink a coffee. A very hard knot to untie….but now I have understood that it is a Fermi Problem…and I am ready to take up the challenge!

So, if I have been able to intrigue you….keep waiting for the next post!


12 risposte a "How many piano tuners are there in Chicago?"

    • Sanssarcasm 3 Feb 2013 / 10:52

      Probably because of the Chicago School for Piano Technology. They put out 5-20 graduates a year. Many stay in the area

      • Cristina Da Rold 3 Feb 2013 / 10:57

        Maybe,I didn’t think about that. Actually it was just an example made by Enrico Fermi to explain his idea of what a “Fermi Problem” should be.
        Anyway, thanks for your comment, and for having visited my website!
        have a good day

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