# The mass of humanity

Ever since Malthus, there has been a concern about overpopulation.  I thought it would be an interesting excercise to see how much space the human population actually takes up.  For example, how many oil tankers would it take to carry around the volume of humanity if converted to liquid.  Let’s say there are 6 billion people on the planet and the average mass per person is 100 kg (this is an overestimate).  Hence, the upper bound on the mass of humanity is $10 ^{12}$ kg, or a billion metric tons.  Given that we are mostly water, we can assume that this is about $10^{12}$ litres.  Taking the cube root gives $10^4\times .1$ metres or a kilometre.  Thus, if we liquefied the mass of all humans, it would fit in a cube whose sides are a kilometre long.   The largest oil tankers can carry about five hundred thousand metric tons, so two thousand oil tankers could cart around all of humanity.  To put that into perspective, according to Wikipedia, the current fleet of oil tankers moves around 2 billion metric tons a year, so half the world’s fleet could carry around the world’s population.

Now, how much area would we take up if we were to stand side by side.  Let’s say 6 people can fit into a square metre of space, then we would all be able to fit into a billion square metres or 1000 square kilometres, about the size of  Hong Kong (according to Wolfram Alpha), or we could all fit 4 to a square metre  onto the island of Oahu in Hawaii.  If we each wanted about 100 square metres of space, then we would take up about a million square kilometres or about twice the area of France.  Wolfram Alpha also tells me that there is about $1.5\times 10^7$ square kilometres of arable land in the world.  If we assume that a square kilometre can feed 1000 people (10 people per hectare), then that puts the capacity of the earth at 15 billion people.

## 8 thoughts on “The mass of humanity”

1. Tom Chou says:

I for one, need much, much more lebensraum….

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2. Given that there are 150 million square kilometres of land on the earth, you could have about 20 hectares. That’s pretty good I would say.

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3. girlwithaquestion says:

This totally answered my question and the answer was unexpected but thorough. thank you google.com

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4. […] because people want to get the very low prices for goods and products without having to look at the mass of humanity which is very depressing for normal people to see. Therefore, I am one to say that I think that […]

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5. […] population is nearing 7 billion and will perhaps hit 9 billion by 2050.  In a previous post,  I estimated that the earth could feed up to 15 billion based on the amount of arable land and […]

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6. Ed says:

If we all grow food at home we could easily double world production

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