Annual revenue at a Starbucks: the power of Fermi approximations


What is a Fermi approximation? 

The only thing that physicists like more than dimensional analysis is a good order of magnitude estimation, also known as a Fermi problem or Fermi approximation. A classic is the piano tuner problem: “How many piano tuners are in the city of Chicago?” 

If you were to just guess a number in response, there’s a pretty good chance that you’ll be way off. You probably know there aren’t 1 million or only 10 piano tuners in the city, but it’s hard to know if 100, 1,000, or 10,000 tuners feels most correct. How do we tackle this problem? The basic principle behind answering this question and others like it is to guess factors of the answer, rather than immediately guess the answer itself. 

“Factoring” your answer

The crux of guessing factors related to your answer is to involve many different points of approximation in order to have your underestimations and overestimations cancel out. As an example, let’s consider a more relatable question: “How much does a typical Starbucks make in one year?” 

We could think of the answer as a product in the following way: 

  1. The amount of money a Starbucks makes in a year is the amount it makes per day, times 365, if we assume every day is about the same. 
  2. The amount of money a Starbucks makes in a day is about the amount it makes per hour, times the number of open hours.
  3. The amount made per hour is about equal to the number of transactions in that hour times the amount per transaction.

We could summarize the above as: 

(Money per year) = 365 (number of open hours) (transactions per hour) (money per transaction)

We’ve successfully taken our problem from estimating something which is hard to wrap our minds around (the amount of money in a whole year) to something most of us can probably imagine (the amount of money per Starbucks transaction and the frequency of transactions).

Let’s put some numbers in!

  1. A typical Starbucks transaction for each customer is probably around 5 dollars. Some people buy only drinks (probably less than 5), some get a drink and a snack (probably more than 5), so it averages out.
  2. Let's say Starbucks processes an order every 2 minutes (based on the wait times I've seen). That comes out to 30 orders an hour. Usually, coffee shops are open for about 12 hours a day, from early morning to afternoon. As such, Starbucks processes about 360 orders a day.
  3. It might be a stretch, but let’s say that Starbucks is open every day, so we'd get about 131,400 orders a year. With each order priced at 5 dollars, that comes out to 657,000 dollars in revenue!

The actual annual revenue of a Starbucks is averaged at 808,000 dollars, so our approximation isn’t too bad at all! 

Why does this work?

Let’s try to understand this point earlier about our overestimations and underestimations cancelling out. How exactly does that work? 

If we call our factors a and our answer X, then our answer takes the form:

Screen Shot 2021-05-24 at 1.59.29 PM

It’s likely that we tend to overestimate certain factors, such as the number of transactions per hour, and underestimate others, such as the price per transaction. Perhaps we are a factor of 3 too large on one and a factor of 3 too small on the other. The final answer has no extra factors at all because 3 and ⅓ would cancel out! 

The magic of Fermi approximations lies in this concept, making this simple technique extremely powerful for getting order of magnitude estimations. You can now answer questions like “How many pieces of paper could a package of pencil lead cover?” or “How many new cars does a dealership sell per month, on average?”

Physics – from high school physics to physics at the graduate level – can be quite challenging. That's why we maintain a staff of physics PhDs and working professionals who are committed to the art of teaching. There is no course or standardized test that we do not have extensive experience teaching. Want to learn more?

Contact us!

Checking your answers in physics

What physics equation sheets can do for you and what they really, really can’t

Working with lenses and mirrors - how to draw a ray diagram


academics MCAT study skills SAT medical school admissions expository writing English college admissions GRE GMAT LSAT MD/PhD admissions chemistry math physics ACT writing biology language learning strategy law school admissions graduate admissions MBA admissions creative writing homework help MD test anxiety AP exams interview prep summer activities history philosophy career advice premed academic advice ESL economics grammar personal statements study schedules admissions coaching law statistics & probability PSAT computer science organic chemistry psychology SSAT covid-19 CARS legal studies logic games USMLE calculus parents reading comprehension 1L Latin Spanish dental admissions DAT engineering excel political science French Linguistics Tutoring Approaches chinese research DO MBA coursework Social Advocacy case coaching classics genetics kinematics secondary applications skills verbal reasoning ISEE academic integrity algebra business business skills careers diversity statement geometry medical school mental health social sciences trigonometry 2L 3L Anki EMT FlexMed Fourier Series Greek IB exams Italian MD/PhD programs STEM Sentence Correction Zoom amino acids analysis essay architecture art history artificial intelligence astrophysics athletics biochemistry capital markets cell biology central limit theorem chemical engineering chromatography climate change clinical experience curriculum data science dental school finance first generation student functions gap year harmonics health policy history of medicine history of science information sessions integrated reasoning international students investing investment banking mba meiosis mitosis music music theory neurology phrase structure rules plagiarism presentations pseudocode sociology software software engineering teaching tech industry transfer typology virtual interviews work and activities writing circles