My four year old recently asked me whether everyone on the planet could fit in one city.

It turns out that if each person occupied one square meter, an area of about 7,200 km² (2780 mi²) would be required. (See revisions below based on current 2016 population estimates.)

This is more than 3x the land area of Tokyo, 5x the land area of Los Angeles, more than 9x the land area of New York City proper. So no, the world’s population couldn’t fit in any single city proper. But if you counted the greater metro areas of these cities, then yes, they could easily.

But since my boy just visited his grandparents who live on the Big Island of Hawai’i (total land area 10,430 km²), I told him they could all fit on the island with room to spare.

His Grammie objected that I hadn’t considered the lava flows or the mountains or craters:

You mean standing up the snowy slopes of Mauna Kea and down into hot lava Halema’uma’u crater or is this just mushy math?

Challenged, I did the math myself.

Assume each person occupies 1 square meter, all in a square area.

Wolfram Alpha now uses 7.13 billion as the world population (2013 figure). The square root of 7.13 billion = 84,439. Meaning an area of 84,439 meters by 84,439 meters or 7,130 km² would be required (*i.e.*, the same as world population / 1 million square meters because 1km² = 1 million m²)

By the same logic, a 2016 population estimate of 7.4 billion would then take 7,400 km². This difference makes the conclusion below a little tighter, but everyone could still fit.

Since the land area of the big island is 10,430 km², there would be 3,030 km² (or about 29% of the total land area) to spare.

The total area of Mauna Kea is 22.8% of the island’s land area. In the past 25 years, only 4% of the island’s land area has been covered by lava (150 mi² or 388.5 km²). The total area of the Halema’uma’u Crater is less than 1 km² and is almost certaintly already included in that 4%. Therefore, let’s say that Mauna Kea + lava flows + Halema’uma’u crater = 27% of land area.

*Conclusion*: the world’s population could stand side by side, each occupying one square meter each, and not stand on any lava flows since 1983, or the crater, or any of Mauna Kea, and still leave about 2% of the island’s land area unoccupied.

I’ll concede that this assumes people would have to stand on the roofs of buildings and on roads, etc. I’m not sure how to estimate total developed land area, but I think it would be safe to assume that would be more than that “vacant” 2% but less than the 23% consumed by Mauna Kea (which we excluded). So I believe it would be fair to assume that we could compensate for development by putting people some of the way up Mauna Kea but not to the point they freeze at the summit.

I’m also ignoring Mauna Loa here. But by the same logic, if we exclude just the frozen peaks of both Mauna Kea and Mauna Loa, there would be be considerable room to spare.

Now the question is, would *all that extra weight* (just over one trillion pounds assuming average human weight of 137 lbs) make the island *sink*?