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Fermi Estimation

Estimate a number you can't look up by breaking it into parts you can guess.

Use it whenyou need a number quickly and there is no data to look up.

Origin
Enrico Fermi, 1940s
Time
10 to 20 min
Works
Solo
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§1

Abstract

Some questions look impossible without data, like how many piano tuners work in Chicago. A Fermi estimate breaks the question into a chain of smaller quantities you can each guess within a range, such as the number of households and how often a piano needs tuning. Multiply them out and you're often within a factor of a few of the actual answer.

It works because errors tend to cancel, with some guesses too high and others too low. Giving each factor a low and a high value also shows you how uncertain the result is. Enrico Fermi was known for doing these in his head.

§2

Method

  1. 01

    Write the question

    Say exactly what you're estimating and in what unit. For example, the number of piano tuners working in Chicago.

  2. 02

    Break it into factors

    Write a chain of quantities that multiply or divide to give the answer, and check that the units cancel.

  3. 03

    Put bounds on each factor

    Give each one a low and a high value you'd be surprised to fall outside.

  4. 04

    Combine

    Multiply the middle values for the estimate, and the lows and highs for the range.

  5. 05

    Sanity-check

    Compare with anything you already know. If one factor carries most of the uncertainty, that's the one to look up.

§3

When to use it

  • You need a rough number quickly to decide if something's worth looking into.
  • A claim or forecast seems too big or too small and you want to check it.
  • You're sizing a market or a budget before any real data exists.
§4

Common pitfalls

  • Forgetting units. If they don't cancel to the unit of the answer, a factor is missing or wrong.
  • Ranges that are too narrow. Honest bounds are wide, often a factor of three or more.
  • Taking the ordinary average of low and high. In a chain of multiplications, the geometric mean is the better middle.
  • Treating the result as a measurement. It tells you the order of magnitude and little more.
§5

Origin and references

Attributed to Enrico Fermi (1940s).

  1. Weinstein, L., & Adam, J. A. (2008). Guesstimation. Princeton University Press.
  2. Tetlock, P. E., & Gardner, D. (2015). Superforecasting: The Art and Science of Prediction. Crown.
§6

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