Fermi estimation
/ FEHR-mee /
Fermi estimation is the art of getting a rough but sensible answer to a seemingly impossible question using only common sense and a few reasonable guesses, with no data and no internet. It is named after the physicist Enrico Fermi, famous for estimating the yield of the first atomic bomb by tossing scraps of paper into the blast wave. The classic exercise: how many piano tuners are there in Chicago?
The method is to break a hard question into a chain of easier ones you can each guess to within a factor of a few, then multiply the estimates and track the units. For the piano tuners: population of Chicago (about 3 million) leads to households (about 1 million), a fraction with a piano (say 1 in 20), pianos tuned per year, tuners' working days, tunings per day, and so on. Individual guesses are shaky, but because some are too high and others too low, the errors tend to partly cancel, and the final order of magnitude usually lands close.
Fermi estimation is not about the exact number; it is about knowing whether an answer should be dozens or millions before you commit to a plan or trust a computation. Physicists, engineers and scientists use it constantly to sanity-check results and to decide whether a project is even worth attempting.
How many piano tuners in Chicago? 3 million people, about 1 million households, maybe 1 in 20 owns a piano (50,000 pianos), each tuned once a year; a tuner does about 4 a day, 250 days a year (1000 per year). That needs roughly 50 tuners, and the phone book confirms a number of that order.
Chain reasonable guesses; over- and under-estimates partly cancel.
The magic works because errors tend to cancel, but only if your guesses are honest and roughly independent. One wildly biased assumption can still throw the whole estimate off.