Rough Numbers

Enrico Fermi liked to ask questions such as how many piano tuners work in a large city. No one knows, yet a sensible answer is within reach. Guess the city’s population, how many households own a piano, how often a piano is tuned, and how many tunings one tuner can do in a year.

Each step is a rough guess, but the errors tend to point both ways, so they partly cancel. The result will not be exact. It will tell you whether the answer is around ten, a hundred or ten thousand.

The method is useful whenever a claim sounds too large or too small. Estimating gives you a check. If a claim is far from your rough figure, either your guess is off or the claim needs a second look.

The piano tuners

A report says that a city of two million people has three thousand full-time piano tuners. Noor is doubtful and estimates for herself.

Two million people is about eight hundred thousand households. Say one in fifty has a piano, which is sixteen thousand pianos, tuned once a year. A tuner does about a thousand tunings a year. That suggests around sixteen tuners, not three thousand, and she asks the report’s author for the source.

Try this today Estimate how many coffees your town drinks each day by splitting it into steps, and write your steps down.