Fermi Estimation

In a city of 10 million people, roughly how many cups of bubble tea are sold in a day?

At first glance there's no way to know. But the physicist Enrico Fermi had a habit: when facing a quantity that seemed impossible to estimate, he broke it into a few numbers he could roughly guess and multiplied them together.

Estimate step by step

• City population: 10 million.
• People who drink bubble tea (mostly young and middle-aged adults): about 60%, or 6 million.
• They average one cup every 5 days, so about 20% drink one on any given day: 6 million × 20% = 1.2 million.
• One cup each time: about 1.2 million cups.

Check it another way

Estimate again from the supply side: roughly one bubble-tea shop per 2,000 people gives 5,000 shops for 10 million people. At 250 cups per shop per day, 5,000 × 250 = 1.25 million cups.

Both routes land in the same order of magnitude, so you can be more confident the answer is "around a million cups."

Why multiplying rough numbers works

Each step might be too high or too low, but the errors often point in different directions and partly cancel out. Fermi estimation isn't after a precise figure; it's after the right order of magnitude: 100,000, a million, or 10 million?

If you really can't pin a step down, say "somewhere between 10 and 1,000," take the geometric mean of the ends: √(10 × 1,000) = 100, not the arithmetic mean of 505.

Using it in forecasts

Many forecasting questions hide a quantity: "Will this movie gross over 500 million yuan in its opening week?" "Will the company app pass 100,000 downloads this month?" Use a Fermi estimate to get a central value, then see how far the target is from it. That gives your probability a solid footing.

In the estimation tree below, fill in your estimate at each level and it multiplies them automatically. Try a few different breakdowns and compare.