97 Things Every SRE Should Know

Chapter 61. Fewer Spreadsheets, More Napkins

Jacob Bednarz

 

Napkin math is a process of performing calculations that provide an answer within a degree of magnitude of accuracy when you’re unable (or don’t need to) gather exact specifics, instead relying on using simplified assumptions. This is useful for confirming the viability of an option or narrowing the range of possibilities without spending hours or days on more complex calculations.

The kinds of estimation problems well suited for this are formally known as Fermi problems. A famous example estimates the number of piano tuners in a given city.

Assume that Chicago has a population of three million people, and each household contains on average two people. Say, one in 20 houses has a piano, and that it needs to be tuned only annually. Guess that piano tuners work eight hours per day, five days a week for 50 weeks per year (so, 250 days), and that each piano takes two hours to tune.

From here, we can quickly scratch out the following:

• Assume Chicago has a population of ~3,000,000

• Chicago has ~2 people per household

• (1,500,000 households) / (20 households with a piano) = 75,000 pianos in Chicago

• (8 hours per day) / (Tuning takes 2 hours) x (250 days per year) = 1000 pianos tuned per year

• (75,000 pianos in Chicago) / (1000 piano tunes a year) = 75 piano tuners in Chicago

Of course, there are most likely not 75 piano tuners ...