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.

### References

Cooper, Lance. *Making Estimates in Research and Elsewhere*.

Fermi, Enrico. *My Observations During the Explosion at Trinity on July 16, 1945*.

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