Fermi estimation: order-of-magnitude from anchored factors
Bracket the answer with order-of-magnitude factors that are easy to estimate. Geometric mean of low and high gives you within one order of magnitude.
Method · Fermi Estimation
Intro
Fermi estimation answers questions like “how many X in city Y?” by decomposing the unknown into a product of factors you each have rough intuition about. The recipe: (i) write the unknown as a multiplicative chain of 3–5 ratios, (ii) anchor each factor to something you know, (iii) multiply (in logs to propagate uncertainty cleanly). The goal is the right order of magnitude, not the right number — and the discipline is being honest about which factors you actually have evidence for.
✓ Intro · expand
Try first (productive failure)
Before the worked example: spend 60 seconds taking your best shot at this.
A guess is fine — being briefly wrong about a problem makes the explanation
land harder when you read it. This appears once per tutorial; skip
if you already know the trick.
60s
✓ Try first · expand
Worked example
How many piano tuners are there in Chicago?
✓ Worked example · expand
Practice 1 of 3Type a fraction, decimal, or expression — mathjs parses it.
✓ Practice · expand
Reflection
Why does Fermi estimation work as well as it does — what is the “magic” that makes a product of rough guesses converge on a not-too-rough answer? When does it <em>fail</em>, and what is the warning sign in the problem?