Skip to main content
FERMI DAILY
← Back to today's problem

Fermi estimation examples

Six classic problems, worked step by step

The best way to learn Fermi estimation is to watch it done. Each example below breaks a question into a few factors you can guess, multiplies them, and lands on an answer within the right order of magnitude. The assumptions are rough on purpose — change any one and see how much the result moves. New to the idea? Start with the guide to Fermi questions.

1. How many piano tuners work in Chicago?

  1. Chicago has about 3 million people, or roughly 1 million households.
  2. Assume about 1 in 20 households owns a piano: ~50,000 pianos (plus some in schools and churches).
  3. A piano is tuned about once a year: ~50,000 tunings per year.
  4. A tuner does ~4 tunings a day × 250 working days ≈ 1,000 tunings a year.
  5. 50,000 ÷ 1,000 ≈ 50 piano tuners.

Estimate: About 50 — anywhere from 20 to 150 is a defensible range.

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

  1. A resting heart rate is about 70 beats per minute.
  2. A day has about 1,440 minutes, so ~100,000 beats per day.
  3. A year has 365 days: ~37 million beats per year.
  4. Over an 80-year life: 37 million × 80 ≈ 3 billion beats.

Estimate: About 3 billion beats.

3. How many golf balls fit inside a school bus?

  1. Assume a bus interior of about 2.4 m wide × 1.8 m tall × 10 m long ≈ 43 m³.
  2. Seats and fittings take up space; call the usable volume ~35 m³.
  3. A golf ball is ~4.3 cm across, so a cube around it is ~80 cm³.
  4. Random packing fills about 64% of space, so each ball effectively uses ~125 cm³.
  5. 35 m³ = 35,000,000 cm³; ÷ 125 ≈ 280,000 golf balls.

Estimate: Roughly 300,000 golf balls.

4. How many school buses are there in the United States?

  1. The US has about 330 million people, and roughly 1 in 6 are school-age: ~55 million students.
  2. Assume about half ride a bus: ~27 million riders.
  3. A bus carries ~50 students per route, and many run two routes: ~100 students per bus.
  4. 27 million ÷ 100 ≈ 270,000 buses; add spares and special-needs buses.

Estimate: About 300,000 to 500,000 school buses.

5. How many pizzas are eaten in the US each day?

  1. Assume the average American eats pizza about once every 2 weeks.
  2. 330 million people ÷ 14 days ≈ 24 million pizza meals a day.
  3. A pizza serves about 3 people, so 24 million ÷ 3 ≈ 8 million pizzas.

Estimate: Several million pizzas a day — about 8 million with these assumptions.

6. How much water does one person use at home in a year?

  1. A shower uses about 60 litres (8 minutes × ~8 litres per minute).
  2. Toilet: ~5 flushes × 6 litres ≈ 30 litres a day.
  3. Cooking, drinking, dishes, laundry and taps: another ~60 litres a day.
  4. Total ≈ 150 litres per day × 365 ≈ 55,000 litres a year.

Estimate: Around 50,000 litres (about 50 cubic metres) a year.

These are illustrative estimates built from rough assumptions, not sourced statistics. Ready to try one yourself? Play today's problem or browse the archive.