If every human lined up facing north with their arms outstretched and touching, at what latitude would this closed circle be?
Mike Follows
Sutton Coldfield, West Midlands, UK
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If the world’s population stood on the equator with outstretched arms and fingers touching, there would be enough people to circle Earth more than 300 times.
The arm span of a person is close to their height, and the average height of an adult Homo sapiens is 168.5 centimetres.
The average radius of Earth is 6371 kilometres, but because the planet is slightly oblate (fatter around its middle), the equatorial circumference is 40,075 km. According to worldometers.info, the world population was an unfeasibly precise 8,053,332,437 on 11 August 2023. If there were no children, only adults, this population could wrap itself around the equator almost 340 times. By integrating a graph of height against age, our estimate of the average height of a human falls to 155.9 cm and the number of loops of the equator drops to 313.
This all assumes that everyone is standing at sea level on a smooth surface, with the oceans removed so that they could all breathe. Taking account of topography – the ups and downs of Earth’s surface – would reduce the number of loops by a little.
There is an urban myth that Earth would be smoother than a billiard ball if it were shrunk down to the same size. The truth is that it would be rounder than a billiard ball, despite being oblate, but it wouldn’t be as smooth. On the scale of a billiard ball, Everest and the Mariana trench would depart from sea level by between 40 and 50 micrometres respectively. Given that a human finger can feel wrinkles as small as 10 nanometres, a billiard-ball sized Earth would feel like very fine micro-grit sandpaper.
Colin Davies
Sheffield, South Yorkshire, UK
The circumference of Earth at its equator is 40,075 kilometres. For 8.05 billion people to fit along this circumference, each would somehow have to squeeze into a gap of just under 5 millimetres. Perhaps it would help if we all breathed in.
The distance from fingertip to fingertip with arms stretched out sideways is clearly going to vary with age and stature. For an upper-bound estimate we could use the traditional measure known as a fathom, which was originally defined in just such a way for an adult male and is nowadays standardised as 6 feet, or around 1.83 metres. Multiplying this distance by the global population figure gives a total of 14.7 million kilometres, which, if we all stood in a ring, would form a circle with a radius of 2.34 million kilometres. That is a little over six times the radius of the moon’s orbit around Earth. If you waved to a friend standing opposite you in this ring, it would take almost 16 seconds before they could see the gesture – that is how slowly light travels.
Robert Fizek, who asked the question, writes from Newton, Massachusetts, which apparently lies at a latitude of 42.34° north. Earth’s circumference at this latitude would, by simple trigonometry, be some 29,600 kilometres.
Allowing 1.83 metres of arm-swinging space per person, you could stand some 16.2 million people at that latitude in a north-facing ring (which, according to the most recent reliable-looking estimate I could quickly find, would be around 2.3 times the population of Massachusetts).
Simon Rundle
Shepton Mallet, Somerset, UK
While the general solution for an arbitrary band around an arbitrary sphere involves some maths, the specific solution is simpler. A population of 8 billion spaced at 1-metre intervals will circumnavigate the equator (40,000 km) 200 times. As 75 per cent of this path is underwater, if the population can be persuaded to do this, it may also provide a solution for the planet’s current environmental difficulties.
Brad Kuhns
Via Twitter
It would vary over time. Everyone over an ocean would drown, which would decrease the population, and everybody standing on land would have to march north until they got to pure ice. Then the population would be stable.
Simon Strong
Hertford, UK
A back-of-the envelope calculation shows that if you divide the length of the equator by the world population, then each person only has 5 millimetres of room to stand in, so this isn’t going to work. However, if the population of the UK (67 million) stood around the equator, each person would have about 60 cm, so standing shoulder to shoulder would be possible. Or you could fit the world population around the circumference of the sun (4.4 million km) and give each person about 55 cm.
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