Estimating like a pro

How many pianos are there in your city? How many gummy bears fit in a jar? You can't look up questions like these, and yet you can answer them: by estimating cleverly. The physicist Enrico Fermi was famous for estimates like this, and his best known one asked: how many piano tuners work in Chicago? That is why they are called Fermi questions today. The best part: the method behind it can be learned.

Thinking in orders of magnitude

When estimating, you don't ask: is it 8317 or 8318? You ask: is it closer to 100, 1000 or 10000? These steps of ten are called orders of magnitude. If you hit the right order of magnitude, you've already won the estimation game. A day has 86400 seconds, for example: for an estimate it's enough to know it's closer to 100000 than to 10000 or a million.

Breaking it into estimable parts

The core of every Fermi question: break the unguessable into parts you can estimate. Pianos in a city of 100000 people? Estimate: about 2 people per household, so 50000 households. Maybe 1 in 50 households has a piano, which would be 1000 pianos. Each single estimate is rough, but together they usually land in the right order of magnitude, because errors up and down tend to cancel out.

Checking for plausibility

At the end you check your result: can that be right? 1000 pianos for 100000 residents means 1 piano per 100 people. Sounds reasonable. If you had ended up with 100000 pianos, one per person, you would know immediately that something is off. This plausibility check helps you everywhere, by the way, from checking receipts to questioning headlines.