50 Fermi Estimation Practice Problems with Solutions

Fermi estimation is a skill, not trivia. You don't need to know the answer — you need to know how to build it. These 50 problems span markets, science, and everyday life, each with a worked solution showing the reasoning chain.

Work through them in order. The anchor patterns you develop on problems 1–20 accelerate the rest.

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Markets and Finance

1. What is the total market capitalization of the US stock market?

Approach: ~6,000 listed companies, but the distribution is heavily skewed toward the top. The S&P 500 alone accounts for ~$40T. Add small and mid caps: total is ~$50–55T.

Answer: ~$50T

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2. How many shares of Apple stock trade per day?

Approach: Apple's market cap ≈ $3T, stock price ≈ $200 → ~15B shares outstanding. Large-cap daily turnover is roughly 0.5–0.7% of shares outstanding. 15B × 0.007 ≈ 105M shares/day.

Answer: ~80–120M shares/day

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3. What is the daily trading volume of the US equity market in dollars?

Approach: ~$50T total market cap, average daily turnover ≈ 0.4%. $50T × 0.004 = $200B/day. Cross-check: ~10B shares/day × average price $25 = $250B/day.

Answer: ~$200–250B/day

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4. How many options contracts trade on US exchanges daily?

Approach: Options volume has grown dramatically. Currently ~40–50M contracts/day across all US exchanges. Each contract represents 100 shares of the underlying.

Answer: ~40–45M contracts/day

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5. What is the daily revenue of Visa and Mastercard combined?

Approach: Global card payment volume ≈ $25T/year. Visa + Mastercard collect ~0.10–0.15% in network fees. $25T × 0.00125 / 365 ≈ $85M/day each, ~$170M combined.

Answer: ~$150–200M/day combined

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6. How many Bloomberg terminals are active globally?

Approach: Bloomberg terminal costs ~$25,000/year. Bloomberg's estimated revenue is ~$10B+/year. $10B / $25K ≈ 400,000 terminals. Consistent with public estimates.

Answer: ~350,000–400,000 active terminals

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7. What is the total value of all gold ever mined?

Approach: ~200,000 metric tons mined in all of history. Gold price ≈ $3,000/troy oz; 32,150 troy oz per metric ton. 200,000 × 32,150 × $3,000 ≈ $19T.

Answer: ~$18–20T

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8. How much money flows through the US payment system daily?

Approach: Fedwire (large-value transfers) alone processes $4–5T per day. ACH adds ~$100B. CHIPS adds another $2T. Total large-value payments: ~$5–7T/day.

Answer: ~$5T/day

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9. What is Warren Buffett's annual income from dividends alone?

Approach: Berkshire holds ~$300B in publicly traded equities. Average dividend yield ≈ 1.5%. $300B × 0.015 = $4.5B/year in dividends received.

Answer: ~$4–5B/year

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10. What is the US federal budget deficit per day?

Approach: Annual federal deficit ≈ $1.5–2T. Per day: $2T / 365 ≈ $5.5B/day. The US borrows ~$5 billion every single day.

Answer: ~$5B/day

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Science and the Physical World

11. How many atoms are in a grain of sand?

Approach: A grain of sand weighs ~1 mg = 10⁻³ g. SiO₂ molar mass ≈ 60 g/mol. Moles = 10⁻³/60 ≈ 1.7×10⁻⁵ mol. Atoms = 1.7×10⁻⁵ × 6×10²³ × 3 ≈ 3×10¹⁹ atoms.

Answer: ~10¹⁹ atoms

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12. How far does light travel in one nanosecond?

Approach: Speed of light ≈ 3×10⁸ m/s. In 1 ns = 10⁻⁹ s: 3×10⁸ × 10⁻⁹ = 0.3 meters. About 1 foot. This is why network latency matters in HFT — 1ms of latency is 300 km of light travel.

Answer: ~30 cm (about 1 foot)

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13. How many seconds old are you at age 30?

Approach: 30 years × 365.25 days × 24 hours × 3,600 seconds = 30 × 31,558,000 ≈ 946 million seconds ≈ 10⁹ seconds.

Answer: ~1 billion seconds

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14. How many piano tuners are in Chicago?

Approach: Chicago population ~2.7M. ~2.5 people/household = ~1M households. ~1 in 20 has a piano = 50,000 pianos. Each tuned once/year. A tuner does ~4/day × 250 days = 1,000/year. 50,000 / 1,000 = 50 tuners. (The original Fermi problem.)

Answer: ~50 piano tuners

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15. How many times does a human heart beat in a lifetime?

Approach: ~75 beats/min × 60 × 24 × 365 × 80 years = 75 × 525,600 × 80 ≈ 3.15 billion beats.

Answer: ~3 billion heartbeats

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US Economy and Society

16. How much does the US spend on coffee per year?

Approach: 330M Americans, ~50% drink coffee daily. 165M × ~$3/cup × 365 ≈ $180B purchased. But home brewing (cheaper) accounts for a substantial share. Total market (retail + foodservice) ≈ $100–120B/year.

Answer: ~$100B/year

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17. How many cars are registered in the US?

Approach: 330M people, ~2 adults per household = ~130M households. Most households own 1–2 vehicles. ~280M registered vehicles in the US.

Answer: ~280M cars

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18. How much does the US spend on healthcare per year?

Approach: US GDP ≈ $27T. Healthcare ≈ 18% of GDP. $27T × 0.18 ≈ $4.9T. Cross-check: ~$14,000/person × 330M = $4.6T.

Answer: ~$4.5–5T/year

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19. How many people fly on US airlines per day?

Approach: ~900M domestic passengers/year ÷ 365 ≈ 2.5M/day. Including international originating in the US: ~3M total.

Answer: ~2.5–3M passengers/day

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20. What is the total US student loan debt?

Approach: ~44M borrowers. Average balance ~$38,000. 44M × $38K ≈ $1.7T. Cross-check: ~$1.7T is confirmed by federal data.

Answer: ~$1.7T

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Technology and Internet

21. How many emails are sent per day worldwide?

Approach: ~4B email users. 20 legitimate emails/day each = 80B. But spam is ~80% of total email volume. Total: ~80B / 0.2 ≈ 350–400B emails/day.

Answer: ~350B emails/day

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22. How many iPhones has Apple sold in total since 2007?

Approach: ~250M/year in recent years, ramping up from zero in 2007. Rough average across 17 years: ~150M/year. 150M × 17 ≈ 2.5B iPhones total sold.

Answer: ~2.3–2.5B iPhones

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23. What is the total value of all Bitcoin in existence?

Approach: ~19.7M BTC in existence (approaching the 21M cap). At $70,000/BTC: 19.7M × $70K ≈ $1.4T.

Answer: ~$1–1.5T (price-dependent)

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24. How many Google searches happen per day?

Approach: Google processes ~8.5B searches/day. Population 8B × ~1 search/day each = 8B/day. Consistent with Google's published figures.

Answer: ~8–9B searches/day

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25. How large is the global data center market by annual revenue?

Approach: AWS alone does ~$100B/year. Azure and GCP add another $100B+ combined. Colocation and private data centers add more. Total: ~$300–400B/year in data center services revenue.

Answer: ~$300B/year

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Probability and Expected Value

26. If you roll two standard dice, what is the expected value of their product?

Approach: E[X × Y] = E[X] × E[Y] for independent random variables. E[single die] = (1+2+3+4+5+6)/6 = 3.5. E[product] = 3.5 × 3.5 = 12.25.

Answer: 12.25

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27. In a room of 30 people, what's the probability that at least two share a birthday?

Approach: P(all different) = (365/365) × (364/365) × ... × (336/365). This product ≈ 0.294. P(at least one shared) = 1 − 0.294 ≈ 70.6%. (The famous birthday problem — most people drastically underestimate this.)

Answer: ~70.6%

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28. If you flip a fair coin 10 times, what's the probability of exactly 5 heads?

Approach: C(10,5) / 2¹⁰ = 252 / 1,024 ≈ 24.6%.

Answer: ~25%

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29. A stock is at $50. It can go to $60 or $40 with equal probability. What's the fair value of a $55 call?

Approach: Payoff at $60: call is worth $5. Payoff at $40: call is worth $0. EV = 0.5 × $5 + 0.5 × $0 = $2.50. (No discounting assumed.)

Answer: $2.50

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30. How many times must you flip a coin to have a 99% chance of at least one tails?

Approach: P(no tails in n flips) = (1/2)ⁿ. Want (1/2)ⁿ ≤ 0.01. n ≥ log(0.01)/log(0.5) = 6.64. Round up: n = 7 flips gives P ≈ 99.2%.

Answer: 7 flips

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Energy and Environment

31. How many gallons of gasoline does the US consume per day?

Approach: ~280M cars × ~1 gallon/day average (some days zero, some days multiple) ≈ 280M gallons/day from passenger vehicles. Add trucks and commercial: ~360M gallons/day total.

Answer: ~360M gallons/day

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32. How much CO₂ does a typical car emit per year?

Approach: Average ~15,000 miles/year at ~25 mpg = 600 gallons. 1 gallon of gasoline → ~8.9 kg CO₂. 600 × 8.9 ≈ 5,340 kg ≈ 5.3 metric tons CO₂/year.

Answer: ~5 metric tons CO₂/year per car

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33. What is the installed solar capacity in the US in gigawatts?

Approach: US has been adding ~25–30 GW/year. By 2026, total installed capacity is ~150–175 GW. This generates roughly 4–5% of US electricity.

Answer: ~150 GW

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34. How much energy does the US use per year, in terms that make sense?

Approach: US population 330M. Average American uses ~80 MWh/year equivalent (electricity + transportation + heating). 330M × 80 MWh ≈ 26,000 TWh ≈ 100 quadrillion BTU (quads) — the unit EIA uses.

Answer: ~100 quads/year

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35. How many trees are planted in the US per year?

Approach: US timber industry plants 1.5–2B seedlings/year to replace harvested trees. Add urban/conservation plantings: ~3B trees planted/year. (Harvested: ~700M/year.)

Answer: ~3B trees planted/year

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Food and Consumer Goods

36. How many hamburgers does McDonald's sell per day globally?

Approach: ~40,000 McDonald's worldwide. Average ~1,500 customers/day. ~40% order a burger. 40,000 × 1,500 × 0.4 = 24M burgers/day.

Answer: ~15–25M burgers/day

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37. What is the annual revenue of Starbucks?

Approach: ~36,000 stores globally. Corporate stores average ~$2M/year; licensed stores less. Blended average ~$1.2M. 36,000 × $1.2M = $43B. (Starbucks reports ~$36B — some licensed revenue counted differently.)

Answer: ~$36–40B/year

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38. How many gallons of milk does the US produce per year?

Approach: ~9M dairy cows in the US. Average production ~8 gallons/cow/day. 9M × 8 × 365 ≈ 26B gallons/year. (USDA reports ~23B gallons — average is lower.)

Answer: ~23B gallons/year

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39. How much does the US spend on pet food per year?

Approach: ~90M dogs + ~94M cats = ~184M pets that eat commercial food. Average spend ~$600/year per dog, ~$300/year per cat. (90M × $600) + (94M × $300) = $54B + $28B ≈ $82B/year.

Answer: ~$70–80B/year (APPA confirms ~$65B)

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40. What is the global annual production of steel?

Approach: Steel is used in everything: construction, cars, appliances, infrastructure. Global: ~1.9B metric tons/year. China produces ~50% of global steel.

Answer: ~1.9B metric tons/year

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Space and Scale

41. How many atoms are in the human body?

Approach: Body mass ~70 kg, mostly water (H₂O, molar mass 18). 70,000g / 18 g/mol ≈ 3,900 mol of water. × 6×10²³ molecules/mol × 3 atoms/molecule ≈ 7×10²⁷ atoms.

Answer: ~7×10²⁷ atoms

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42. How long would it take to drive to the moon at highway speed?

Approach: Moon distance ≈ 384,000 km. At 100 km/h: 384,000 / 100 = 3,840 hours ≈ 160 days of non-stop driving.

Answer: ~160 days

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43. If you stacked all the US M2 money supply in $1 bills, how tall would the stack be?

Approach: M2 ≈ $21T = 2.1×10¹³ bills. A $1 bill is ~0.1 mm thick. Stack height: 2.1×10¹³ × 0.0001 m = 2.1×10⁹ m = 2.1 million km — about 5× the distance to the moon.

Answer: ~2 million km — 5× the Earth-Moon distance

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44. How many molecules of water are in a glass of water?

Approach: A glass ≈ 250 mL = 250g. Molar mass H₂O = 18 g/mol. Moles = 250/18 ≈ 13.9. Molecules = 13.9 × 6×10²³ ≈ 8.3×10²⁴ molecules.

Answer: ~8×10²⁴ molecules

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45. How many red blood cells are in the human body?

Approach: ~5 million RBCs per microliter of blood. Blood volume ~5 liters = 5×10⁶ microliters. Total: 5×10⁶ × 5×10⁶ = 2.5×10¹³ RBCs = 25 trillion.

Answer: ~25 trillion red blood cells

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Market Intuition Checks

These five are the "market fluency" checks that appear in trading interviews:

46. What is the US federal government's annual tax revenue?

US GDP ~$27T. Federal tax revenue ~17% of GDP. $27T × 0.17 ≈ $4.6T. (IRS data confirms ~$4.9T for 2024.)

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47. What is the market cap of Goldman Sachs?

Goldman has ~46,000 employees, ~$50B in annual revenue, and trades at roughly 12× earnings. Net income ~$12B. Market cap ~$130–170B.

Answer: ~$150B

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48. What is the annual GDP of New York City?

NYC population ~8M. GDP per capita ≈ $130,000 (very high for a dense financial center). $130K × 8M = $1.04T. NYC is the largest metro economy in the US.

Answer: ~$1T

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49. How many people work in finance in New York City?

NYC financial sector employs ~350,000 in direct financial activities. Broadly including fintech, insurance, and related professional services: ~500,000.

Answer: ~500,000 people in NYC finance broadly

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50. What fraction of the S&P 500's total market cap is the top 10 companies?

Approach: Top 10 companies (Apple, Microsoft, NVIDIA, etc.) each have market caps of $1–3T. Combined ~$18–20T. S&P 500 total ≈ $40T. Top 10 ÷ total ≈ 45–50%.

Answer: ~35–40% (actual as of 2025: ~35%, concentration has been rising)

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Patterns to Internalize

After 50 problems, three patterns should be automatic:

Chain multiplication. Most answers are built as: (base count) × (rate or fraction) × (value per unit). Identify these three components first.

Reference anchors. US population 330M, GDP $27T, S&P 500 $40T, federal debt $36T — know these cold. Almost every market estimation problem chains back to one of them.

Two-direction sanity checks. If you estimated from the demand side, check from the supply side. If answers don't converge within a factor of 2–3, you have a wrong assumption somewhere.

Commit to a range. "~$100B, maybe $80–130B" is far more useful than "$94.7B" (false precision) or "between $1B and $10T" (no information).

Practice these daily with Fermiq's drill — the patterns compound fast.