Fermi estimation: decompose, anchor, sanity-check

You can’t know the number — but you can build it from a handful of guesses you can make, and land within a factor of ten.

The idea

“How many cups of coffee does one Starbucks sell in a day?” No one knows off-hand. But you can guess the pieces: seats, how often they turn over, hours open, drinks per customer. Multiply them and you get an answer.

The magic is that your guesses don’t all miss the same way. Some run high, some run low, and when you multiply, the errors partly cancel — so even rough anchors land within an order of magnitude of the truth. Round to one significant figure, then check it against something you know.

How it works

1. 1Decompose. Break the unknown into factors you can actually guess. Cups per day is seats, turns per hour, open hours, and drinks per customer.
2. 2Anchor each factor. Pick a defensible number for each — a value you could justify out loud. Say it, don’t agonise.
3. 3Multiply, then round to one significant figure. The product is your estimate. Drop the false precision: 1,470 becomes ~1,000.
4. 4Sanity-check against a known reference. Reach the same number a second, independent way. If both land in the same band, trust it.

Worked through with the default anchors:

seats × turns/hr × hours × drinks/customer
  25  ×    3      ×  14   ×    1.4          = 1,470

round to one significant figure  ->  ~1,000 cups/day

Cross-check (public numbers, another decomposition):
  revenue ~ $36B  ÷  ~$5 / drink   =  ~7.2B drinks / year
  ~7.2B  ÷  ~38,000 stores  ÷  365  =  ~500 cups / store / day

Two independent paths: ~1,000 and ~500 — same order of
magnitude (10^3). That agreement is the sanity check.

Why the errors cancel: if each of four factors is independently off by up to 2×, the product’s error grows like the square root of the number of factors, not their sum. The stress test above bears it out — nearly every run stays within a single order of magnitude.

When to use it

Fits	The trade-off
Market sizing, capacity and load, “how many…” brain-teasers, gut-checking a spreadsheet or a vendor’s claim — anywhere you need a defensible number fast.	It gives you the order of magnitude, not a precise figure. Don’t use a Fermi estimate where being off by 3× would be costly — there, go measure.

Watch out for

• False precision. Reporting “1,470” implies a rigour you don’t have. Round to one significant figure — “about a thousand.”
• Correlated errors. The cancellation only works if your factors are independent. If you low-ball two things that move together, both misses stack instead of cancelling.
• Double-counting or gaps. Make sure the factors multiply to the whole and don’t overlap. Seats and turns already capture throughput — don’t also multiply by “number of registers” and count the same customers twice.
• Skipping the sanity-check. The second, independent estimate is what catches a factor you fat-fingered. Never present a Fermi number without one.
• Anchoring on a suspicious round number. If a factor conveniently “feels like 100,” interrogate it — that’s often where a 10× error hides.

Worked example

“How many piano tuners work in Chicago?” — the classic. Decompose: ~3 million people, ~2 or 3 per household so ~1 million households, maybe 1 in 20 owns a piano so ~50,000 pianos, each tuned about once a year so ~50,000 tunings a year. A tuner does maybe 4 a day, ~250 days a year, so ~1,000 tunings per tuner per year. That gives ~50,000 ÷ 1,000 = ~50 tuners. Every factor is a guess, yet the answer lands in the right band — and published counts for Chicago are indeed in the dozens. That’s Fermi: not exact, but honestly close.

Check yourself

Prep Room · say your anchors out loud as you go — the interviewer is grading the decomposition, not the digits.