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We have only one planet, it’s true, and there are ever more of us crowding onto its surface. With six billion humans and counting, surely we must be running out of land—if not on which to live, then on which to grow the enormous amounts of food required to feed us all. As evidence, we are reminded of the large swaths of the planet mired in poverty, a tragedy that is used to justify any number of illiberal policies, from Maoist one-child population control laws to Stalinist food rationing meant to stretch out our meagre and dwindling resources.

Thankfully, these fears are unjustified. The advent and improvement of air travel and modern communications technologies have certainly made the planet seem smaller—we can zip to the Far East in a matter of hours, or send electronic documents anywhere in the world in a matter of seconds—but it’s still the same gigantic ball of rock it has always been. The Earth is really staggeringly large; too large, in fact, to grasp intuitively. Of course, six billion is also too large a number to grasp intuitively. Only mathematics can help us understand if we are truly running out of space.

Our planet has a surface area of approximately 510 million square kilometres, of which just under 30% (149 million sq. km) is land area. How many people can the Earth support? According to Scientific American, “With current farming techniques, a little less than half an acre can grow enough food to feed one person.” One square kilometre contains roughly 247 acres, and so can feed approximately 500 people. If all of the land on Earth were suitable for food production, our planet could therefore support a population of some 73.5 billion people (149 million times 500). Of course, not all land is suitable for agriculture, but thankfully we don’t need it to be. Our current population of six billion could be fed on just 12 million square kilometres of agricultural land, an area slightly larger than the United States. Even at nine billion people (the downwardly-revised population peak we are set to hit by 2050)(1), we would only need 18 million square kilometres, representing just 12% of the land on Earth, or an area about the size of Russia. Furthermore, this figure assumes unrealistically that no further improvements in farming techniques will be invented over the next five decades.

1. Although it is true that there are more of us than ever, the 2004 UN projections show that population growth is slowing and total population is on course to top out at around nine billion by mid-century, far fewer than previously thought.