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There is a facebook post that says the entire population of the planet could live in 2000 square foot houses just in the state of Alaska.

Some research shows that there are roughly 1585682383 households on the planet. Alaska is 663,300 mi².

I dont think Im doing the math correctly..... households x 2000^2 Then converting that number to miles^2

user382568
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  • You don't need to square 2000, the units are already in square feet. – Mathily Oct 25 '16 at 17:13
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    Don't square the number $2000$. A $2000$ square foot house is not $2000 \times 2000$ feet. It might be $80 \times 25$ feet. – David K Oct 25 '16 at 17:13
  • Also consider the possibility that the facebook post assumed the houses would have multiple floors. A house of $2000$ square feet floor area might have a "footprint" much less than $2000$ square feet. – David K Oct 25 '16 at 17:14
  • I make it each person in the world could be allocated 3000 square feet of Alaska, since a square mile is $5280^2 = 27878400$ sq ft – Cato Oct 25 '16 at 17:15
  • One square mile is 5280^2=27,878,400 square feet. – Thomas Andrews Oct 25 '16 at 17:15
  • For us all to 'live' in the state of Alaska with all houses right next to each other might be difficult ... :) – Bram28 Oct 25 '16 at 17:15
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    "Roughly 1585682383"? – Brian Tung Oct 25 '16 at 17:16
  • Whoever conducted that research shouldn't be trusted. No one with any idea what they're doing would give that many significant digits. – user2520938 Oct 25 '16 at 17:20

2 Answers2

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So the total area of all the houses would be $$ 2000\text{ sq.ft.}\times 1\,585\,682\,383 = 3\,171\,364\,766\,000\text{ sq.ft.} \approx 3.171\cdot 10^{12}\text{ sq.ft.} $$ Now, a square mile is roughly $2.788\cdot 10^7 \text{ sq.ft}$. How many square miles do all those hoseholds take up? We get $$ \frac{3.171\cdot 10^{12}\text{ sq.ft.}}{2.788\cdot 10^7 \text{ sq.ft}/\text{sq.mi.}} = 1.137\cdot 10^5\text{ sq.mi.} $$ which, compared to Alaska's total area of $6.633\cdot 10^5 \text{ sq.mi.}$ means that we only use a sixth of the total area. Each of the one and a half bilion houses can come with roughly $10\,000$ square feet of back gardens before you fill up the entirety of Alaska. Alternatively, you could fill Alaska with such houses wall-to-wall, and there would be roughly a house to each person in the world, if all the houses are only ground floors. Start building the $2000$ square foot houses with several floors, and you save enough ground space to make streets.

Arthur
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  • Several times I started to write a comment but you kept incorporating the things I thought of into your answer before I managed to post anything! I can only add that the colder parts of North America, as far as I've observed, $2000$ square foot houses almost invariably do have multiple floors, so I think it's reasonable to assume the houses in the question would. – David K Oct 25 '16 at 17:28
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$1$ mile is $5280$ feet. So 1 square mile is $5280^2 = 27,878,400$ square feet. If one house is $2000$ square feet, the you can have $27878400 / 2000 = 13939.2$ houses per square mile. So in $ 663,300$ square miles you can have $ 663,300 \cdot 13939.2 = 9,245,871,360$ houses.

This, of course assumes that you have no space between houses and that the terrain allows for houses all over.

Thomas
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