How big a box would you need for everybody?

Well, how much space do people take up? Assuming an average human mass of 65 kg, and a density of close to 1 (since we only just float), a person occupies 65,000 cubic centimeters. In theory you could pack about 15 people in a cubic meter (or 1,000,000 cubic centimeters). That seems like a lot, doesn’t it? Let’s check. It turns out the record for stuffing smallish undergraduates into a telephone booth is 22, and a phone booth is about 1.3 cubic meters inside. And remember, the folks near the bottom of the Big Box will be somewhat…compressed. Nevertheless, let’s assume an average of 13 people per cubic meter, since those near the top won’t be so packed so tightly.

The current world population is 6.6 billion. At 13 people per cubic meter, that’s a 507,692,308 m^{3} box; if it’s a cube, the Big Box is 798 m on each interior side. Say we make it an even 800 m (which allows for another 56 million people, probably as many as will be born by the time we’ve wrangled everyone inside). Don’t ask me how thick the walls would need to be; I’m not an engineer.

Exactly how big is a box 800 m a side? That’s half a mile. The World Trade Center was 417 m high. The box would take up 32 city blocks in Manhattan; it’d fit neatly into a fifth of Central Park.

The world’s population thus occupies an eighth of a cubic mile. All together we’d weigh 430 metric megatons. The pressure on the poor folks at the bottom would be half a ton per square inch, or 64 atmospheres–in fact, what you’d feel nearly half a mile deep in the ocean. The sea of humanity indeed.

Obviously you’d want to be one of the last inside the Big Box. How many people would be left standing when it was filled? The area of the top of the box is 640,000 m^{2}, and a common estimate for crowd density is 6 people to the square meter. That means nearly 4 million people get to stand on top of everybody else; coincidentally, about the population of New Zealand. Lucky Kiwis!