Abstract


  • 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


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

Time / trading

  • Seconds/day โ‰ˆ 86,400 (โ‰ˆ10โต)
  • Minutes/day โ‰ˆ 1,440
  • Trading days/year โ‰ˆ 252 (โ‰ˆ250)
  • Weeks/year โ‰ˆ 52
  • Work hours/year (1 FTE) โ‰ˆ 2,000

Scale of people & money

  • World pop โ‰ˆ 8ร—10โน
  • US pop โ‰ˆ 3.3ร—10โธ
  • Chicago (city) โ‰ˆ 2.7ร—10โถ
  • NYC โ‰ˆ 8โ€“9ร—10โถ
  • US GDP โ‰ˆ 2.5ร—10ยนยณ USD
  • World GDP โ‰ˆ 1ร—10ยนโด USD

Physics-lite

  • g โ‰ˆ 10 m/sยฒ
  • c โ‰ˆ 3ร—10โธ m/s
  • atm โ‰ˆ 10โต Pa
  • Earth radius โ‰ˆ 6.4ร—10ยณ km, circumference โ‰ˆ 4ร—10โด km

Everyday

  • Walking speed โ‰ˆ 1.4 m/s (โ‰ˆ5 km/h)
  • 1 L water โ‰ˆ 1 kg
  • Byte math: 1 GB โ‰ˆ 10โน bytes

Logs / constants (mental math)

  • ฯ€โ‰ˆ3, eโ‰ˆ2.7, ln(10)โ‰ˆ2.3, logโ‚‚10โ‰ˆ3.32, ln2โ‰ˆ0.693

Estimation


  • 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 ~90โ€“95%)