Fermi Problem

Abstract

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• Fermi problems are about making a rough estimate when exact data is unknown.
• The trick is to break big questions into smaller factors we can guess.
• By working in powers of 10 and combining factors, over- and under-estimates usually balance out, leading to a reasonable answer.a

Fermi Anchors

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• Some common numbers to act as entry points for making a reasonable estimation

Time / trading

• Seconds/day ≈ 86,400 (≈10⁵)
• Minutes/day ≈ 1,440
• Trading days/year ≈ 252 (≈250)
• Weeks/year ≈ 52
• Work hours/year (1 FTE) ≈ 2,000

Scale of people & money

• World pop ≈ 8×10⁹
• US pop ≈ 3.3×10⁸
• Chicago (city) ≈ 2.7×10⁶
• NYC ≈ 8–9×10⁶
• US GDP ≈ 2.5×10¹³ USD
• World GDP ≈ 1×10¹⁴ USD

Physics-lite

• g ≈ 10 m/s²
• c ≈ 3×10⁸ m/s
• atm ≈ 10⁵ Pa
• Earth radius ≈ 6.4×10³ km, circumference ≈ 4×10⁴ km

Everyday

• Walking speed ≈ 1.4 m/s (≈5 km/h)
• 1 L water ≈ 1 kg
• Byte math: 1 GB ≈ 10⁹ bytes

Logs / constants (mental math)

• π≈3, e≈2.7, ln(10)≈2.3, log₂10≈3.32, ln2≈0.693

Estimation

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• Answer with an interval [low, high]. You score when the truth lands inside; narrower intervals score better if they still cover the truth
• Strategy beats guessing: start wider when unsure, then tighten as your decomposition stabilizes. Match the confidence level requested (often ~90–95%)