Fermi Estimate of Daily Breaths Across Sleep, Rest and Exercise
Company: Google
Role: Product Manager
Category: Product / Decision Making
Difficulty: medium
Interview Round: Other
Estimate how many breaths we take in a day.
```hint Not one rate all day
Breathing speed changes over 24 hours. Split the day into a few states with clearly different rates before you multiply anything.
```
### Clarifying Questions
- Should "we" mean one typical adult, or everyone alive combined?
- Is the target a healthy adult on an ordinary day, or should children, who breathe faster, be included?
- How precise does the answer need to be: the right order of magnitude, or within roughly 20%?
### What a Strong Answer Covers
- A clear equation that splits the day by activity level
- Breathing-rate and duration assumptions, each labeled and briefly justified
- Clean arithmetic with sensible rounding
- A sanity check against an independent anchor
- How the estimate changes for other groups, and which assumption it is most sensitive to
### Follow-up Questions
- How would your number change for a newborn, or for a marathon runner on race day?
- Extend the estimate to everyone on Earth. Which assumption moves the total most?
- If a wearable maker wanted the real figure, how would you measure it instead of estimating it?
Overview: A classic estimation question asking how many breaths people take in a day. It tests building a clear equation, labeling assumptions about breathing rates during sleep, rest and exercise, doing the arithmetic cleanly, sanity-checking the result, and scaling the estimate from one person to the whole population.