# Estimate like Fermi

25 Apr 2018

On 16 July 1945 the New Mexico sky lit up from the world’s first atomic bomb blast. Ten miles away, scientist Enrico Fermi tore up a sheet of paper. As the shock wave hit, he dropped the bits of paper which were carried away by the blast. He measured the distance the paper travelled, consulted a table, and estimated the bomb yield at 10 kilotons of TNT. Later the precise yield was calculated: 18.6 kilotons.

Fermi’s estimate was was off by a factor of two, good enough for the field.

## What is a Fermi estimate?

A Fermi estimate or Fermi problem uses simple calculations to approximate a more complex equation. Fermi estimates are useful for sanity-checking a complicated calculation to make sure it’s not spewing gibberish. Or for getting a quick estimate instead of waiting for a more precise answer.

## Learn to estimate

You can learn to make estimates like Fermi.

• Know the domain. Fermi was a PhD physicist who understood how shock waves expand and how the pressure drops off with distance.
• Do the math. Fermi didn’t just throw some paper in the air and make a wild guess. Before going out into the field he calculated a lookup table that gave the bomb yield for a given distance.
• Break up the problem. If you wanted to estimate the number of piano tuners in Chicago, you’d estimate the number of households, the percentage of those households that have a piano, how often a piano needs to be tuned, and how many pianos a piano tuner can tune in one year. This should lead you to a reasonable answer.
• Simplify. Use round numbers, invent spherical cows, whatever it takes.
• Calculate bounds. Use the upper and lower extremes of your estimates to calculate the upper and lower bounds of the problem. We should be able to say something like: There are probably between 2 and 8 piano tuners in Chicago.

## Why do Fermi estimates work?

A Fermi estimate works because it’s composed of several estimates of terms. Some of the terms are over-estimated, some are under-estimated so the errors cancel out.

Cooper, Lance. Making Estimates in Research and Elsewhere.

Rhodes, Richard. The Making of the Atomic Bomb. Simon and Schuster, 1986.