Deep Dive8 minUpdated 2025-01-21

Fermi Estimation for Case Interviews: Quick Guide

Make smart assumptions fast. Fermi decomposition tactics, key benchmarks to memorize, and rounding rules that won't break your case answer.

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Perfect accuracy is rarely possible—or even expected—in case interviews. What matters is making reasonable assumptions and arriving at sensible estimates through clear logic.

Why Estimation Matters More Than Exact Answers

In real consulting, you rarely have perfect data. Clients pay for:

  • Structured thinking under uncertainty
  • Reasonable approximations that guide decisions
  • Speed to insight, not decimal precision

Interviewers test the same skills. A well-reasoned estimate that's 20% off beats a precise-looking number with flawed logic.

Fermi Decomposition

Named after physicist Enrico Fermi, this technique breaks one big unknown into several smaller, estimable pieces.

The Formula:

Big Unknown = Factor 1 × Factor 2 × Factor 3 × Factor 4

Example: "How many golf balls fit in a school bus?"

Break it down:

  • Bus volume: 8m × 2m × 2m = 32 cubic meters = 32,000 liters
  • Golf ball volume: sphere ~40ml (4cm diameter)
  • Packing efficiency: ~65% (spheres don't pack perfectly)

Calculate:

32,000L × 0.65 / 0.04L = ~520,000 golf balls

Even if each estimate is off by 20%, the final answer is in the right ballpark.

Safe Benchmarks to Memorize

Having anchor points makes estimation faster and more accurate.

Population

  • US: 330M | California: 40M | NYC: 8M
  • Germany: 84M | UK: 67M | France: 68M
  • World: 8B | China/India: 1.4B each

Economics

  • US GDP: $25 trillion | US median income: $75K
  • Minimum wage (US): ~$15/hr | Average new car: $50K
  • Average home price (US): $400K

Time

  • Hours in a year: ~8,760 (≈9,000)
  • Working hours/year: ~2,000
  • Minutes in a day: 1,440 (≈1,500)

Business

  • Typical gross margin: 30-50%
  • SaaS gross margin: 70-80%
  • Retail net margin: 2-5%

Rounding Rules That Don't Break the Case

When 10% error is fine:

  • Market sizing
  • Back-of-envelope ROI
  • Preliminary breakeven

When precision matters:

  • Final recommendation numbers
  • Anything client-facing
  • Comparing close alternatives

Safe rounding strategies:

  • Round to 1 significant figure during calculation, refine at end
  • Round some up, some down (errors cancel)
  • State your rounding: "I'll use 100 for simplicity"

Checking if Your Answer "Smells Right"

The Newspaper Test

Would this number sound crazy in a news headline? "Company spends $500B on paperclips" → probably wrong.

The Per-Capita Test

Divide by population. Does $X per person make sense? $10B market / 330M people = $30/person.

The Comparison Test

Compare to known benchmarks. Is your answer 10x or 0.1x what you'd expect?

5 Estimation Practice Questions

Q1: How many pizzas are consumed in the US daily?

Hint: 330M people, maybe 1-2 slices/week average?

Q2: What's the annual revenue of all US barbershops?

Hint: How many shops? Customers per day? Average ticket?

Q3: How many tennis balls are used at Wimbledon each year?

Hint: Courts, matches, balls per match?

Q4: What's the market size for baby strollers in Germany?

Hint: Births per year, price, replacement cycle?

Q5: How many flights take off from JFK daily?

Hint: Runways, time per takeoff, operating hours?

Linking Estimation Back to Business Insight

The number alone isn't the answer. Always connect to the business question:

❌ "The market is $2B"

✅ "The market is $2B, which means a 5% market share—realistic for a new entrant—would generate $100M revenue, enough to justify the $50M investment"

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