# Fermi Estimation

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

Chapter III, Problem solving · 3.14 · Origin: Enrico Fermi (1940s) · Time: 10 to 20 min · Solo

**Use it when** you need a number quickly and there is no data to look up.

Interactive workspace: https://kogu.tools/tools/fermi-estimation

## 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.

## Method

1. **Write the question.** Say exactly what you're estimating and in what unit. For example, the number of piano tuners working in Chicago.
2. **Break it into factors.** Write a chain of quantities that multiply or divide to give the answer, and check that the units cancel.
3. **Put bounds on each factor.** Give each one a low and a high value you'd be surprised to fall outside.
4. **Combine.** Multiply the middle values for the estimate, and the lows and highs for the range.
5. **Sanity-check.** Compare with anything you already know. If one factor carries most of the uncertainty, that's the one to look up.

## 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.

## 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.

## References

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