Order of Magnitude Estimation (Fermi)

Fermi estimation or order of magnitude estimation is a back-of-the-envelope technique where estimates to difficult problems are found by breaking up the larger question into smaller, likely still unknown parts, making a guess (with error bars) and then multiplying the parts together. A standard Fermi question would be “How many piano tuners are there in Chicago?” Breaking the question down into constituent parts, you come up with some still hard questions:

  1. How many pianos are there in Chicago?
    1. How many people are there in Chciago?
    2. How many Pianos per person?
  2. How many piano tuners are needed per piano?
    1. How long does it take to tune a piano?
    2. How many hours a year does a piano tuner work?

While precision on any of these answers aside from the easiest (how many hours a year does a piano turner work) will be difficult, we can get rough guesses1. We can also set lower and upper bounds on our guess2.

Fermi estimation works because errors tend to cancel each other out if there isn’t an underlying bias.


Tetlock, P. E. & Gardner, D. Superforecasting: The Art and Science of Prediction. (Crown, New York, 2015).
lukeprog. Fermi Estimates.

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