Fermi questions: how to estimate what nobody knows
A Fermi question is a problem you do not know the exact answer to, but can work out by estimating. Break it into smaller steps, estimate each one roughly and multiply the results. The goal is not an exact number but the right order of magnitude: hundreds or millions. It is named after physicist Enrico Fermi, famous for such estimates.
A Fermi question in 4 steps
- Be clear about what exactly you are counting and in which units.
- Break the question into steps you can estimate: how many people, how often, how many pieces.
- Estimate each step roughly. An order of magnitude is enough, like 10, 100 or 1,000.
- Multiply and check that the result makes sense. If not, find the step that is off.
Example: how many piano tuners are there in Chicago?
The classic Fermi question. All numbers below are estimates, not facts, and that is the point.
| People in Chicago | about 3,000,000 |
|---|---|
| Households (about 2–3 people each) | about 1,000,000 |
| Households with a piano (about one in twenty) | about 50,000 |
| Tunings a year (one per piano) | about 50,000 |
| Tunings one tuner manages a year (4 a day, 250 days) | about 1,000 |
| Piano tuners | about 50 |
The answer “a few dozen” is useful even without the exact number. It is not hundreds, and not one.
FAQ about Fermi estimates
Why is it called a Fermi question?
After the Italian-American physicist Enrico Fermi, winner of the 1938 Nobel Prize in Physics. He was known for quickly and surprisingly well estimating quantities he had no exact data for.
How accurate should a Fermi estimate be?
A good estimate lands in the right order of magnitude. Being no more than twice too high or too low is a very good result. In Fynal such a guess scores about 70 points out of 100.
What are Fermi estimates good for?
They help you quickly check whether a number makes sense, in the news, at work or when planning. They also come up in job interviews, for example at consulting firms.
Where can I practise Fermi questions?
In Fynal. Every day you get three new Fermi questions, and after your guess you see the answer, the calculation and how others guessed.