Fermi Estimate of the Sworn Police Workforce in the United States
Company: Meta
Role: Product Manager
Category: Product / Decision Making
Difficulty: medium
Interview Round: Other
Estimate how many police officers there are in the United States. Walk through your reasoning step by step, stating each assumption and the numbers you use.
```hint Tie the count to the work
Consider what drives how many officers a community needs, and remember that police work runs around the clock, every day of the week.
```
### Clarifying Questions
- Should the count include only officers serving today, or everyone who has ever served?
- Does "police officer" mean sworn officers with arrest powers only, or also civilian staff, reserves and recruits still in training?
- Which agencies are in scope: city and county police only, or also state police and federal law enforcement?
- Should part-time officers be counted, and if so, as people or as full-time equivalents?
### What a Strong Answer Covers
- A precise scope for who counts, agreed before any numbers.
- A clear equation that breaks the total into estimable pieces.
- Assumptions stated with round numbers and a reason for each.
- Correct arithmetic, plus a sanity check by a second method or a reference point.
### Follow-up Questions
- How would your estimate change if federal law enforcement agents were included?
- Which assumption is your estimate most sensitive to, and how wide is the plausible range?
- Building on your answer, how would you estimate the number of police patrol cars in the United States?
Overview: A classic estimation prompt asking how many police officers work in the United States. It tests defining exactly who counts, building a structured equation, stating assumptions with round numbers, doing the arithmetic correctly, and sanity-checking the result against a second method or reference point.