Fermi questions with answers

1. At rest, adults breathe about 12 to 20 times a minute. Call it 15.
2. 15 × 60 minutes = 900 breaths an hour.
3. 900 × 24 hours = 21,600.

Answer: About 20,000 breaths a day.

1. Say 8 hours a night.
2. 8 × 365 is about 3,000 hours a year.
3. Over 80 years: 3,000 × 80 = 240,000 hours.

Answer: About 240,000 hours, which is roughly 27 years. That is a third of your life.

1. A year has about 30 million seconds. (See the worked example in our estimation guide.)
2. 30 million × 30 = 900 million.

Answer: Nearly a billion seconds. The exact figure, with leap days, is about 947 million.

1. A pack of 500 sheets is about 5 cm thick.
2. So one sheet is about 0.1 mm.
3. 1,000,000 × 0.1 mm = 100,000 mm = 100 metres.

Answer: About 100 metres, roughly as tall as a 30-storey building.

1. Most people blink about 15 times a minute while awake.
2. You are awake about 16 hours, which is 960 minutes.
3. 15 × 960 = 14,400.

Answer: About 15,000 blinks a day.

1. A resting heart beats about 70 times a minute.
2. 70 × 60 × 24 is about 100,000 beats a day.
3. 100,000 × 365 is about 37 million a year.
4. 37 million × 80 years is about 3 billion.

Answer: About 3 billion heartbeats.

1. Route 1: each beat pushes out about 70 ml. 70 ml × 100,000 beats = 7,000 litres.
2. Route 2: at rest the heart pumps about 5 litres a minute. 5 × 1,440 minutes = 7,200 litres.
3. Two different routes give nearly the same answer. That is a good sign.

Answer: About 7,000 litres a day.

1. Guess how long you spend talking: maybe 2 hours in total.
2. People speak about 130 words a minute.
3. 130 × 120 minutes = 15,600.

Answer: About 16,000 words. A 2007 study that recorded people through the day found almost exactly this, for women and men alike.Source: Mehl and others, Science, 2007.

1. Most numbers below a million are long, like “four hundred and eighty-seven thousand, two hundred and thirty-one”. Allow about 3 seconds each.
2. 1,000,000 × 3 seconds = 3 million seconds.
3. A day has about 86,000 seconds, so that is about 35 days without a break.
4. Counting 8 hours a day, it takes about 100 days.

Answer: About a month non-stop, or three to four months of 8-hour days.

1. The Earth is about 40,000 km around the equator.
2. One walking step is about 0.75 m, so 1 km is about 1,300 steps.
3. 40,000 × 1,300 = 52 million steps.
4. Walking 8 hours a day at 5 km an hour covers 40 km a day, so the trip takes about 1,000 days.

Answer: About 50 million steps, or nearly 3 years of long walking days (if you could walk on water).

1. Say 2 litres a day, counting all drinks.
2. 2 × 365 = 730 litres a year.
3. 730 × 80 years is about 58,000 litres.

Answer: About 60,000 litres. Water weighs 1 kg a litre, so that is about 60 tonnes.

1. A big school bus is about 10 m long, 2.3 m wide and 1.9 m high inside. That is about 44 cubic metres. Take away the seats: call it 40.
2. A golf ball is about 4.3 cm across. Treat it as a cube: 4.3 × 4.3 × 4.3 is about 80 cubic centimetres.
3. 40 cubic metres is 40 million cubic centimetres. 40,000,000 ÷ 80 = 500,000.
4. Balls pack a little better than cubes, so the real number is a bit higher.

Answer: About 500,000 to 700,000 golf balls.

1. Chicago has about 2.7 million people. At 2.5 people per home, that is about 1.1 million homes.
2. Say 1 home in 20 has a piano: about 55,000 pianos.
3. Each piano is tuned about once a year: 55,000 tunings a year.
4. A tuner can do about 4 a day for 250 working days: 1,000 a year.
5. 55,000 ÷ 1,000 = 55.

Answer: About 50 to 100 tuners, once you add schools, churches and concert halls. Nobody keeps an exact count, which is what makes this Enrico Fermi’s most famous question.

1. A teaspoon holds 5 ml, which is 5,000 cubic millimetres.
2. A typical sand grain is about 0.5 mm across. As a cube, that is 0.5 × 0.5 × 0.5 = 0.125 cubic millimetres.
3. 5,000 ÷ 0.125 = 40,000.

Answer: Tens of thousands: about 40,000 to 50,000 grains of medium sand. Fine sand has many more.

1. The Moon is on average about 384,000 km away.
2. At a steady 100 km an hour: 384,000 ÷ 100 = 3,840 hours.
3. 3,840 ÷ 24 = 160 days.

Answer: About 160 days of non-stop driving, or more than a year of 8-hour days.

1. From the first question: about 20,000 breaths a day.
2. A calm breath moves about half a litre of air.
3. 20,000 × 0.5 = 10,000 litres.

Answer: About 10,000 litres a day, more when you move.