Estimation puzzles: work it out from what you know
These are the questions where guessing well beats knowing badly. Each one can be reached from something you already know, by picking a rough number and multiplying carefully. The explanations show the arithmetic rather than just the answer, because the method is the transferable part.
Roughly how much of the Earth's oxygen does the Amazon rainforest actually supply, net?
Close to none
The 'lungs of the Earth' figure of 20 percent is gross photosynthesis. Respiration and decay consume nearly all of it, so the net contribution is close to zero. Ocean plankton dominate long-term oxygen.
Source: Peer-reviewed carbon-cycle analyses; NOAA ocean productivity data
Why do published figures for Britain's coastline vary so much?
It depends on the ruler used
The coastline paradox: a coast is fractal, so measuring with a 100 km ruler gives a much shorter length than a 1 km ruler. Britain's published figures range from about 11,000 to over 19,000 km.
Source: Lewis Fry Richardson, 1961; Benoit Mandelbrot, 1967
Lake Superior holds enough water to cover which of these to a depth of about 30 cm?
The Americas
Superior holds about 12,100 km3. Spread over the Americas' roughly 42 million km2 that gives close to 0.3 m.
Source: US Environmental Protection Agency Great Lakes facts
Roughly what share of land has land directly on the other side of the world?
About 4 percent
Because land clusters in the northern hemisphere, most land is antipodal to ocean. Only about 4 percent has land opposite: mostly Argentina and Chile against China, and Spain against New Zealand.
Source: Antipodal mapping of continental outlines
Roughly how many Olympic swimming pools would Lake Geneva fill?
About 35 million
Lake Geneva holds about 89 km3, or 8.9e13 litres. An Olympic pool is about 2.5 million litres, giving roughly 35 million pools.
Source: Swiss Federal Office for the Environment lake volumes
Roughly how many double-decker buses stacked up would reach the summit of Everest from sea level?
About 2,000
Everest is 8,849 m and a double-decker is about 4.4 m tall. 8,849 divided by 4.4 is roughly 2,000.
Source: Everest height, 2020 joint survey; standard UK bus dimensions
Folding a sheet of paper in half 42 times would make a stack roughly how tall?
Reaching the Moon
Each fold doubles the thickness. 0.1 mm times 2^42 is about 440,000 km, past the Moon's average distance of 384,400 km. Physically folding it that many times is impossible.
Source: Standard exponential arithmetic; typical paper thickness
If all the Earth's water were gathered into a single sphere, roughly how wide would it be?
About 1,400 km across
All water on Earth is about 1.386 billion km3. A sphere of that volume has a diameter near 1,400 km, small enough to sit comfortably inside the continental United States.
Source: USGS 'all the water on Earth' visualisation
How fast is someone standing on the equator moving due to the Earth's rotation?
About 1,670 km/h
The equator is about 40,075 km around and turns once a day, giving roughly 1,670 km/h. At 60 degrees latitude it is about half that.
Source: WGS84 equatorial circumference
Travelling at motorway speed without stopping, roughly how long would crossing Russia take?
About four days
Russia spans about 9,000 km east to west. At 100 km/h non-stop that is about 90 hours, or just under four days.
Source: Russian Federation extent; great-circle arithmetic
If the Earth's land were divided equally, roughly how much would each person get?
About 1.8 hectares
Around 149 million km2 of land divided by about 8 billion people gives roughly 18,600 m2 each, or 1.86 hectares, of which a fraction is habitable and less again is arable.
Source: Land area, CIA World Factbook; population, UN
Roughly how many lightning strikes hit the Earth every second?
About 40 to 50
Satellite detection puts the global rate near 45 flashes a second, concentrated over tropical land. Lake Maracaibo in Venezuela is the single most struck spot on Earth.
Source: NASA lightning imaging sensor data
Which is bigger: the number of people who have ever lived, or the current population, times ten?
They are roughly comparable
Estimates put the total who have ever lived at around 110 billion, against roughly 8 billion alive, so about 7 percent of everyone who has ever lived is alive now.
Source: Population Reference Bureau estimates