Fermi questions: what they are and how to solve them

A Fermi question asks you to estimate something that sounds unanswerable: how many piano tuners are in Chicago, how many breaths you take in a year, how much coffee a city drinks every morning. There's no looking it up — the point is to reason your way to a rough answer from things you already know.

They're named after the physicist Enrico Fermi, who was famous for producing startlingly good estimates from almost no data. The surprising lesson of Fermi questions is that a chain of reasonable guesses usually lands within a factor of ten of the truth — and often much closer.

Why estimating works at all

Individual guesses are unreliable, but their errors don't all push in the same direction. Overestimate one factor and underestimate another, and the mistakes partly offset rather than stack — though that's a tendency, not a guarantee, since a chain of one-directional mistakes can still miss badly. That's why the goal is never the exact number — it's being within the right order of magnitude, and knowing roughly how wrong you might be.

A step-by-step method

1. Pin down the question. Restate it in one measurable unit — per year, per person, per city — so you know exactly what you're counting.
2. Break it into factors. Decompose the answer into a small product of quantities you can guess: people × rate × time. Three to five factors is usually enough.
3. Guess each factor in round numbers. Use powers of ten when you're unsure. It's fine to be off on any single factor; that's what the next step is for.
4. Bracket a range. Instead of one number, give yourself a low and a high you genuinely believe the answer sits between. Honest uncertainty beats false precision.
5. Sanity-check the result. Compare the answer against something familiar. If your estimate for a city's daily coffee consumption exceeds its population a hundredfold, a factor somewhere needs revisiting.

An example, worked the Fermi way

Say the question is how many breaths does a person take in a year? A typical resting rate is around 12–20 breaths per minute. There are about 60 × 24 ≈ 1,500 minutes in a day and 365 days in a year, so roughly 550,000 minutes annually. Multiplying: 15 breaths/minute × 550,000 minutes ≈ 8 million breaths a year. Any answer between a few million and fifteen million is defensible — that's the nature of the game.

Practice one a day

Fermi Daily turns this into a game: one question each day, answered on a logarithmic scale that rewards being within the right order of magnitude rather than exactly right. After you lock in an estimate, you see the step-by-step reasoning behind our own estimate and a reasonable range, so you can compare your chain of assumptions against ours.

Try today's problem or browse the archive of past questions to practice.